Selina Concise Solutions for ICSE Class 10 Mathematics Chapter 3 Shares And Dividend

Question 1. How much money will be required to buy 400, Rs. 12.50 shares at a premium of Rs. 1?
Answer:
Given:
Number of shares to be bought = 400
Nominal value of one share = Rs. 12.50
Premium = Rs. 1

Step 1: Find market value of one share.
Market value = Nominal value + Premium
Market value = Rs. 12.50 + Rs. 1 = Rs. 13.50

Step 2: Find total money required.
Money required = Number of shares × Market value per share
Money required = 400 × Rs. 13.50 = Rs. 5,400

Total money required = Rs. 5,400
In simple words: When shares are sold at premium, you pay more than the face value. Here you pay Rs. 1 extra per share. So total cost becomes higher.

📝 Teacher's Note: Explain that premium means extra money. Like buying a movie ticket for Rs. 100 but paying Rs. 110 because it's a special show. The extra Rs. 10 is premium.

🎯 Exam Tip: Always write "Market value = Nominal value + Premium" first. Then multiply by number of shares. Show each step clearly to get full marks.

Question 2. How much money will be required to buy 250, Rs. 15 shares at a discount of Rs. 1.50?
Answer:
Given:
Number of shares to be bought = 250
Nominal value of one share = Rs. 15
Discount = Rs. 1.50

Step 1: Find market value of one share.
Market value = Nominal value - Discount
Market value = Rs. 15 - Rs. 1.50 = Rs. 13.50

Step 2: Find total money required.
Money required = Number of shares × Market value per share
Money required = 250 × Rs. 13.50 = Rs. 3,375

Total money required = Rs. 3,375
In simple words: Discount means you pay less than the face value. It's like getting a Rs. 100 shirt for Rs. 80. You save Rs. 20 per shirt.

📝 Teacher's Note: Use the example of sale prices in shops. When there's 10% discount, you pay less. Same way, shares at discount cost less than their face value.

🎯 Exam Tip: For discount, subtract from nominal value. For premium, add to nominal value. Don't get confused between the two.

Question 3. A person buys 120 shares at a nominal value of Rs. 40 each, which he sells at Rs. 42.50 each. Find his profit and profit percent.
Answer:
Given:
Number of shares = 120
Nominal value (cost price) = Rs. 40 each
Selling price = Rs. 42.50 each

Step 1: Find total cost price.
Cost price of 120 shares = Rs. 40 × 120 = Rs. 4,800

Step 2: Find total selling price.
Selling price of 120 shares = Rs. 42.50 × 120 = Rs. 5,100

Step 3: Find profit.
Profit = Selling price - Cost price
Profit = Rs. 5,100 - Rs. 4,800 = Rs. 300

Step 4: Find profit percent.
Profit % = \( \frac{\text{Profit}}{\text{Cost price}} \times 100 \)
Profit % = \( \frac{300}{4800} \times 100 = 6.25\% \)

Profit = Rs. 300 and Profit percent = 6.25%
In simple words: He bought shares for Rs. 4,800 and sold them for Rs. 5,100. So he made Rs. 300 profit. That's 6.25% more than what he spent.

📝 Teacher's Note: Relate to buying and selling anything - like buying 10 pens for Rs. 20 and selling for Rs. 25. The profit is Rs. 5 on Rs. 20 investment.

🎯 Exam Tip: Always calculate total cost price and total selling price first. Then find profit. For profit %, use cost price in denominator, not selling price.

Question 4. Find the cost of 85 shares of Rs. 60 each when quoted at Rs. 63.25.
Answer:
Given:
Number of shares = 85
Nominal value = Rs. 60 each
Market value (quoted price) = Rs. 63.25 each

Step 1: Find total cost.
Total cost = Number of shares × Market value per share
Total cost = 85 × Rs. 63.25 = Rs. 5,376.25

Cost of 85 shares = Rs. 5,376.25
In simple words: When shares are quoted at a price, that's the actual price you pay. Here each share costs Rs. 63.25, so 85 shares cost Rs. 5,376.25.

📝 Teacher's Note: Explain that "quoted price" means current market price. Like the price of gold changes daily - that's the quoted price.

🎯 Exam Tip: Use the quoted price (market price) for calculation, not the nominal value. Quoted price is what you actually pay.

Question 5. A man invests Rs. 800 in buying Rs. 5 shares and when they are selling at a premium of Rs. 1.15, he sells all the shares. Find his profit and profit percent.
Answer:
Given:
Total investment = Rs. 800
Nominal value of one share = Rs. 5
Premium when selling = Rs. 1.15

Step 1: Find number of shares bought.
Number of shares = \( \frac{\text{Total investment}}{\text{Nominal value per share}} \)
Number of shares = \( \frac{800}{5} = 160 \)

Step 2: Find selling price per share.
Selling price per share = Nominal value + Premium
Selling price per share = Rs. 5 + Rs. 1.15 = Rs. 6.15

Step 3: Find total selling price.
Total selling price = 160 × Rs. 6.15 = Rs. 984

Step 4: Find profit.
Profit = Selling price - Cost price
Profit = Rs. 984 - Rs. 800 = Rs. 184

Step 5: Find profit percent.
Profit % = \( \frac{184}{800} \times 100 = 23\% \)

Profit = Rs. 184 and Profit percent = 23%
In simple words: He bought 160 shares for Rs. 800. Later sold them for Rs. 984. So he made Rs. 184 profit, which is 23% of his investment.

📝 Teacher's Note: This problem has two steps - buying at nominal value and selling at premium. Make students understand both parts clearly.

🎯 Exam Tip: First find how many shares he bought. Then find selling price with premium. Show all calculations step by step.

Question 6. Find the annual income derived from 125, Rs. 120 shares paying 5% dividend.
Answer:
Note: There seems to be an error in the given solution. The question mentions 125 shares of Rs. 120 each, but the solution uses Rs. 60 and 250 shares. Following the question statement:

Given:
Number of shares = 125
Nominal value per share = Rs. 120
Dividend rate = 5%

Step 1: Find total nominal value.
Total nominal value = 125 × Rs. 120 = Rs. 15,000

Step 2: Find annual dividend.
Annual dividend = 5% of Rs. 15,000
Annual dividend = \( \frac{5}{100} \times 15,000 = Rs. 750 \)

Annual income = Rs. 750
In simple words: Dividend is the profit money that the company gives to shareholders every year. Here the company gives 5% of the face value of shares as dividend.

📝 Teacher's Note: Explain that dividend is like interest on fixed deposit. The company pays a percentage of the share's face value every year to shareholders.

🎯 Exam Tip: Dividend is always calculated on nominal value (face value), not market value. Write the formula clearly: Dividend = Rate% × Nominal value of shares.

Question 7. A man invests Rs. 3,072 in a company paying 5% per annum, when its Rs. 10 share can be bought for Rs. 16 each. Find: (i) his annual income (ii) his percentage income on his investment.
Answer:
Given:
Total investment = Rs. 3,072
Nominal value per share = Rs. 10
Market value per share = Rs. 16
Dividend rate = 5% per annum

Step 1: Find number of shares bought.
Number of shares = \( \frac{\text{Total investment}}{\text{Market value per share}} \)
Number of shares = \( \frac{3,072}{16} = 192 \)

Step 2: Find total nominal value.
Total nominal value = 192 × Rs. 10 = Rs. 1,920

Step 3: Find annual income (dividend).
Annual income = 5% of Rs. 1,920
Annual income = \( \frac{5}{100} \times 1,920 = Rs. 96 \)

Step 4: Find percentage income on investment.
Percentage income = \( \frac{\text{Annual income}}{\text{Investment}} \times 100 \)
Percentage income = \( \frac{96}{3,072} \times 100 = 3.125\% = 3\frac{1}{8}\% \)

(i) Annual income = Rs. 96
(ii) Percentage income on investment = 3.125%
In simple words: He bought shares worth Rs. 3,072 but gets dividend only on face value Rs. 1,920. So his return is Rs. 96 per year, which is 3.125% of his investment.

📝 Teacher's Note: Students often confuse - dividend is on face value but percentage return is on actual money invested (market value).

🎯 Exam Tip: Remember: Number of shares = Investment ÷ Market price. Dividend = Rate% × Nominal value. Percentage return = Dividend ÷ Investment × 100.

Question 8. A man invests Rs. 7,770 in a company paying 5% dividend when a share of nominal value of Rs. 100 sells at a premium of Rs. 5. Find: (i) the number of shares bought; (ii) annual income; (iii) percentage income.
Answer:
Given:
Total investment = Rs. 7,770
Nominal value per share = Rs. 100
Premium = Rs. 5
Dividend rate = 5%

Step 1: Find market value per share.
Market value = Nominal value + Premium
Market value = Rs. 100 + Rs. 5 = Rs. 105

Step 2: Find number of shares bought.
Number of shares = \( \frac{7,770}{105} = 74 \)

Step 3: Find total nominal value.
Total nominal value = 74 × Rs. 100 = Rs. 7,400

Step 4: Find annual income.
Annual income = 5% of Rs. 7,400
Annual income = \( \frac{5}{100} \times 7,400 = Rs. 370 \)

Step 5: Find percentage income.
Percentage income = \( \frac{370}{7,770} \times 100 = 4.76\% \)

(i) Number of shares bought = 74
(ii) Annual income = Rs. 370
(iii) Percentage income = 4.76%
In simple words: He bought 74 shares at Rs. 105 each. The company pays dividend on face value Rs. 100 per share. So he gets Rs. 370 per year, which is 4.76% of his investment.

📝 Teacher's Note: This combines premium calculation, dividend calculation, and return percentage. Make sure students follow each step carefully.

🎯 Exam Tip: When shares are at premium, you pay more but dividend is still on face value only. This reduces your percentage return.

Question 9. A man buys Rs. 50 shares of a company, paying 12% dividend, at a premium of Rs. 10. Find: (i) the market value of 320 shares; (ii) his annual income; (iii) his profit percent.
Answer:
Given:
Nominal value per share = Rs. 50
Premium = Rs. 10
Dividend rate = 12%
Number of shares = 320

Step 1: Find market value per share.
Market value = Nominal value + Premium
Market value = Rs. 50 + Rs. 10 = Rs. 60

Step 2: Find market value of 320 shares.
Market value of 320 shares = 320 × Rs. 60 = Rs. 19,200

Step 3: Find total nominal value.
Nominal value of 320 shares = 320 × Rs. 50 = Rs. 16,000

Step 4: Find annual income.
Annual income = 12% of Rs. 16,000
Annual income = \( \frac{12}{100} \times 16,000 = Rs. 1,920 \)

Step 5: Find profit percent (yield).
Profit % = \( \frac{\text{Annual income}}{\text{Investment}} \times 100 \)
Profit % = \( \frac{1,920}{19,200} \times 100 = 10\% \)

(i) Market value of 320 shares = Rs. 19,200
(ii) Annual income = Rs. 1,920
(iii) Profit percent = 10%
In simple words: He invested Rs. 19,200 and gets Rs. 1,920 per year as dividend. This gives him 10% return on his money.

📝 Teacher's Note: "Profit percent" here means annual yield or return percentage. It's different from capital gain profit when selling shares.

🎯 Exam Tip: Don't confuse profit percent with profit from buying and selling. Here it means yearly return percentage on investment.

Question 10. A man buys Rs. 75 shares at a discount of Rs. 15 of a company paying 20% dividend. Find: (i) the market value of 120 shares; (ii) his annual income; (iii) his profit percent.
Answer:
Given:
Nominal value per share = Rs. 75
Discount = Rs. 15
Dividend rate = 20%
Number of shares = 120

Step 1: Find market value per share.
Market value = Nominal value - Discount
Market value = Rs. 75 - Rs. 15 = Rs. 60

Step 2: Find market value of 120 shares.
Market value of 120 shares = 120 × Rs. 60 = Rs. 7,200

Step 3: Find total nominal value.
Nominal value of 120 shares = 120 × Rs. 75 = Rs. 9,000

Step 4: Find annual income.
Annual income = 20% of Rs. 9,000
Annual income = \( \frac{20}{100} \times 9,000 = Rs. 1,800 \)

Step 5: Find profit percent.
Profit % = \( \frac{1,800}{7,200} \times 100 = 25\% \)

(i) Market value of 120 shares = Rs. 7,200
(ii) Annual income = Rs. 1,800
(iii) Profit percent = 25%
In simple words: He bought shares at discount, so paid less. But dividend is on full face value. This gives him a higher return of 25% per year.

📝 Teacher's Note: When shares are at discount, you get better returns because you pay less but get dividend on full face value.

🎯 Exam Tip: Discount increases your return percentage. Premium decreases it. This is because dividend is always on face value.

Question 11. A man has 300, Rs. 50 shares of a company paying 20% dividend. Find his net income after paying 3% income tax.
Answer:
Given:
Number of shares = 300
Nominal value per share = Rs. 50
Dividend rate = 20%
Income tax rate = 3%

Step 1: Find total nominal value.
Total nominal value = 300 × Rs. 50 = Rs. 15,000

Step 2: Find total dividend.
Dividend = 20% of Rs. 15,000
Dividend = \( \frac{20}{100} \times 15,000 = Rs. 3,000 \)

Step 3: Find income tax.
Income tax = 3% of Rs. 3,000
Income tax = \( \frac{3}{100} \times 3,000 = Rs. 90 \)

Step 4: Find net income.
Net income = Dividend - Income tax
Net income = Rs. 3,000 - Rs. 90 = Rs. 2,910

Net income = Rs. 2,910
In simple words: He gets Rs. 3,000 as dividend but has to pay Rs. 90 as tax. So his final income is Rs. 2,910.

📝 Teacher's Note: Explain that government takes tax on dividend income just like salary. Net income means what you actually keep after paying tax.

🎯 Exam Tip: Always calculate gross dividend first, then deduct tax to get net income. Show both calculations clearly.

Question 12. A company pays a dividend of 15% on its ten-rupee shares from which it deducts income tax at the rate of 22%. Find the annual income of a man who owns one thousand shares of this company.
Answer:
Given:
Nominal value per share = Rs. 10
Number of shares = 1,000
Dividend rate = 15%
Income tax rate = 22%

Step 1: Find total nominal value.
Total nominal value = 1,000 × Rs. 10 = Rs. 10,000

Step 2: Find total dividend.
Dividend = 15% of Rs. 10,000
Dividend = \( \frac{15}{100} \times 10,000 = Rs. 1,500 \)

Step 3: Find income tax.
Income tax = 22% of Rs. 1,500
Income tax = \( \frac{22}{100} \times 1,500 = Rs. 330 \)

Step 4: Find net annual income.
Net income = Dividend - Income tax
Net income = Rs. 1,500 - Rs. 330 = Rs. 1,170

Annual income = Rs. 1,170
In simple words: The company gives Rs. 1,500 dividend but keeps Rs. 330 for government as tax. So the man gets Rs. 1,170 per year.

📝 Teacher's Note: Sometimes companies deduct tax directly from dividend before paying shareholders. This is called TDS (Tax Deducted at Source).

🎯 Exam Tip: When tax rate seems high like 22%, double-check your calculation. Show tax calculation separately to avoid mistakes.

Question 13. A man invests Rs. 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns Rs. 1,200 at the end of the year as dividend, find: (i) the number of shares he has in the company. (ii) the dividend percent per share.
Answer:
Given:
Total investment = Rs. 8,800
Face value (nominal value) per share = Rs. 100
Premium = 10%
Annual dividend earned = Rs. 1,200

Step 1: Find market value per share.
Premium amount = 10% of Rs. 100 = Rs. 10
Market value = Face value + Premium
Market value = Rs. 100 + Rs. 10 = Rs. 110

Step 2: Find number of shares.
Number of shares = \( \frac{\text{Total investment}}{\text{Market value per share}} \)
Number of shares = \( \frac{8,800}{110} = 80 \)

Step 3: Find total face value.
Total face value = 80 × Rs. 100 = Rs. 8,000

Step 4: Find dividend percent per share.
Dividend % = \( \frac{\text{Total dividend}}{\text{Total face value}} \times 100 \)
Dividend % = \( \frac{1,200}{8,000} \times 100 = 15\% \)

(i) Number of shares = 80
(ii) Dividend percent per share = 15%
In simple words: He bought 80 shares at Rs. 110 each. The company paid 15% dividend on face value, giving him Rs. 1,200 total.

📝 Teacher's Note: This is a reverse problem. You know the dividend amount and need to find the dividend rate. Divide dividend by face value to get the rate.

🎯 Exam Tip: When premium is given as percentage, calculate the amount first. Then find market price. Be careful with the calculations.

Question 13. (Continued from previous)
Solution:
Given:
Total investment = Rs. 8,800
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 110

Step 1: Find number of shares purchased.
\( \text{No of shares purchased} = \frac{8800}{110} = 80 \)

Step 2: Find nominal value of shares.
Nominal value of 80 shares = 80 × 100 = Rs. 8,000

Step 3: Find dividend percentage.
Let dividend% = y%
then y% of Rs. 8,000 = Rs. 1,200
\( \frac{y}{100} \times 8,000 = 1,200 \)
\( \implies y = 15\% \)

In simple words: We bought 80 shares for Rs. 8,800. Each share has face value Rs. 100. The company gave Rs. 1,200 as dividend. This means the company paid 15% on the face value.

📝 Teacher's Note: Help students understand that dividend is always calculated on nominal value (face value), not market value. Use a simple example like buying a movie ticket for Rs. 200 but its printed price is Rs. 100.

🎯 Exam Tip: Always write "dividend is calculated on nominal value" in your answer. Show all steps clearly. Write the final answer as "dividend% = 15%".

Question 14. A man invests Rs. 1,680 in buying shares of nominal value Rs. 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate:
(i) the number of shares he buys;
(ii) the dividend he receives annually.
Solution:
Given:
Nominal value of 1 share = Rs. 24
Premium = 12%
Total investment = Rs. 1,680
Dividend% = 15%

Step 1: Find market value of 1 share.
Market value of 1 share = Rs. 24 + 12% of Rs. 24
= Rs. 24 + Rs. 2.88 = Rs. 26.88

Step 2: Find number of shares purchased.
\( \text{No of shares purchased} = \frac{1680}{26.88} = 62.5 \)

Step 3: Find nominal value and dividend.
Nominal value of 62.5 shares = 62.5 × 24 = Rs. 1,500
Dividend = 15% of Rs. 1,500
\( = \frac{15}{100} \times 1,500 = \text{Rs. } 225 \)

In simple words: Premium means the share costs more than its face value. We bought 62.5 shares and get Rs. 225 as yearly dividend from the company.

📝 Teacher's Note: Explain premium as extra cost. Like buying a Rs. 100 note for Rs. 112 because it has value. Students often forget to add premium to find market price.

🎯 Exam Tip: First find market price, then find number of shares. Dividend is always on nominal value. Write both answers clearly: (i) 62.5 shares (ii) Rs. 225.

Question 15. By investing Rs. 7,500 in a company paying 10 percent dividend, an annual income of Rs. 500 is received. What price is paid for each of Rs. 100 share?
Solution:
Given:
Total investment = Rs. 7,500
Nominal value of 1 share = Rs. 100
Dividend% = 10%
Dividend = Rs. 500

Step 1: Find number of shares purchased.
Let number of shares purchased = y
Nominal value of y shares = 100 × y = Rs. (100y)

Step 2: Use dividend formula.
10% of 100y = Rs. 500
\( \frac{10}{100} \times 100y = \text{Rs. } 500 \)
\( \implies y = \frac{500}{10} = 50 \text{ shares} \)

Step 3: Find market value of 1 share.
\( \text{Market value of 1 share} = \frac{7,500}{50} = \text{Rs. } 150 \)

In simple words: The man bought 50 shares for Rs. 7,500 total. So each share cost him Rs. 150, even though its face value is only Rs. 100.

📝 Teacher's Note: Students often get confused between face value and market value. Use coin example - a Rs. 5 coin might sell for Rs. 10 to collectors. Rs. 5 is face value, Rs. 10 is market value.

🎯 Exam Tip: First find how many shares he bought using dividend. Then divide total investment by number of shares to get market price per share. Answer is Rs. 150.

Exercise 3B

Question 1. A man buys 75, Rs. 100 shares of a company which pays 9 percent dividend. He buys shares at such a price that he gets 12 percent of his money. At what price did he buy the shares?
Solution:
Given:
Nominal value of 1 share = Rs. 100
Number of shares = 75
Dividend% = 9%
Return on investment = 12%

Step 1: Find nominal value and dividend.
Nominal value of 75 shares = 100 × 75 = Rs. 7,500
Dividend = 9% of Rs. 7,500
\( = \frac{9}{100} \times \text{Rs. } 7,500 = \text{Rs. } 675 \)

Step 2: Find market price using return formula.
Let market price of 1 share = Rs. y
Then market price of 75 shares = Rs. 75y
Return on investment = 12%
12% of 75y = Rs. 675
\( \frac{12}{100} \times 75y = 675 \)
\( \implies y = \text{Rs. } 75 \)

In simple words: The man gets Rs. 675 dividend. He wants 12% return on his money. So his total investment must be such that Rs. 675 is 12% of it. Each share costs Rs. 75.

📝 Teacher's Note: Return on investment means profit percentage on the money you spend. If you invest Rs. 100 and get Rs. 12 back, your return is 12%.

🎯 Exam Tip: Use the formula: Dividend = Return% × Investment. From this find investment, then divide by number of shares. Answer is Rs. 75 per share.

Question 2. By purchasing Rs. 25 gas shares for Rs. 40 each, a man gets 4 percent profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares?
Solution:
Given:
Nominal value of 1 share = Rs. 25
Market value of 1 share = Rs. 40
Profit% on investment = 4%

Step 1: Find profit on 1 share.
Profit on 1 share = 4% of Rs. 40 = Rs. 1.60

Step 2: Find dividend percentage.
\( \text{Dividend%} = \frac{1.60}{25} \times 100\% = 6.4\% \)

Step 3: Find dividend on 60 shares.
Number of shares purchased = 60
Dividend on 60 shares = 60 × Rs. 1.60 = Rs. 96

In simple words: Each share gives Rs. 1.60 profit. This profit comes from company dividend. Since face value is Rs. 25, the company pays 6.4% dividend. For 60 shares, total dividend is Rs. 96.

📝 Teacher's Note: Profit and dividend are the same thing here. The money you earn from shares is called dividend. This dividend gives you profit on your investment.

🎯 Exam Tip: Find profit per share first, then calculate what percentage this is of nominal value. For 60 shares, multiply profit per share by 60. Answer: 6.4% and Rs. 96.

Question 3. Hundred rupee shares of a company are available in the market at a premium of Rs. 20. Find the rate of dividend given by the company, when a man's return on his investment is 15%.
Solution:
Given:
Nominal value of 1 share = Rs. 100
Premium = Rs. 20
Return on investment = 15%

Step 1: Find market value.
Market value of 1 share = Rs. 100 + Rs. 20 = Rs. 120

Step 2: Find profit using return percentage.
Profit on 1 share = 15% of Rs. 120 = Rs. 18

Step 3: Find dividend percentage.
\( \text{Dividend%} = \frac{18}{100} \times 100\% = 18\% \)

In simple words: The share costs Rs. 120 but face value is Rs. 100. The man gets Rs. 18 profit per share. This means company pays 18% dividend on face value.

📝 Teacher's Note: Premium means extra cost above face value. Students must add premium to face value to get market price. Return is calculated on market price, dividend on face value.

🎯 Exam Tip: Market price = Face value + Premium. Find profit using return%, then find what % this profit is of face value. Answer is 18%.

Question 4. Rs. 50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20 percent.
Solution:
Given:
Nominal value of 1 share = Rs. 50
Discount = 10%
Return on investment = 20%

Step 1: Find market value.
Market value of 1 share = Rs. 50 - 10% of Rs. 50
= Rs. 50 - Rs. 5 = Rs. 45

Step 2: Find profit using return percentage.
Profit on 1 share = 20% of Rs. 45 = Rs. 9

Step 3: Find dividend percentage.
\( \text{Dividend%} = \frac{9}{50} \times 100\% = 18\% \)

In simple words: Discount means the share costs less than face value. Each share costs Rs. 45 but face value is Rs. 50. The profit of Rs. 9 means company pays 18% dividend.

📝 Teacher's Note: Discount is opposite of premium. If face value is Rs. 50 and discount is 10%, market price is Rs. 45. Students often add discount instead of subtracting.

🎯 Exam Tip: Market price = Face value - Discount. Find profit using return%, then calculate what % this is of face value. Answer is 18%.

Question 5. A company declares 8 percent dividend to the share holders. If a man receives Rs. 2,840 as his dividend, find the nominal value of his shares.
Solution:
Given:
Dividend% = 8%
Dividend received = Rs. 2,840

Step 1: Find nominal value of shares.
Let nominal value of shares = Rs. y
Then 8% of y = Rs. 2,840
\( \frac{8}{100} \times y = 2,840 \)
\( \implies y = \text{Rs. } 35,000 \)

In simple words: If 8% of something equals Rs. 2,840, then that something equals Rs. 35,000. This is the total face value of all shares he owns.

📝 Teacher's Note: This is a reverse calculation. Students know dividend amount and percentage, need to find the principal (nominal value). Use simple percentage formula.

🎯 Exam Tip: Use the formula: If x% of y = z, then y = (z × 100)/x. Here y = (2,840 × 100)/8 = Rs. 35,000.

Question 6. How much should a man invest in Rs. 100 shares selling at Rs. 110 to obtain an annual income of Rs. 1,680, if the dividend declared is 12%?
Solution:
Given:
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 110
Dividend% = 12%
Required dividend = Rs. 1,680

Step 1: Find number of shares needed.
Let number of shares purchased = n
Nominal value of n shares = Rs. (100n)
12% of 100n = Rs. 1,680
\( \frac{12}{100} \times 100n = 1,680 \)
\( \implies n = \frac{1,680 \times 100}{12 \times 100} = 140 \)

Step 2: Find total investment.
Market value of 140 shares = 140 × 110 = Rs. 15,400

In simple words: To get Rs. 1,680 dividend, he needs 140 shares. Since each share costs Rs. 110 in market, total investment is Rs. 15,400.

📝 Teacher's Note: First find how many shares give the required dividend, then multiply by market price per share. Students often multiply by face value instead of market price.

🎯 Exam Tip: Find number of shares using dividend formula, then multiply by market price (not face price). Answer is Rs. 15,400.

Question 7. A company declares a dividend of 11.2% to all its share-holders. If its Rs. 60 share is available in the market at a premium of 25%, how much should Rakesh invest, in buying the shares of this company, in order to have an annual income of Rs. 1,680?
Solution:
Given:
Nominal value of 1 share = Rs. 60
Premium = 25%
Dividend% = 11.2%
Required dividend = Rs. 1,680

Step 1: Find market value.
Market value of 1 share = Rs. 60 + 25% of Rs. 60
= Rs. 60 + Rs. 15 = Rs. 75

Step 2: Find number of shares needed.
Let number of shares purchased = n
Nominal value of n shares = Rs. (60n)
11.2% of 60n = Rs. 1,680
\( \frac{11.2}{100} \times 60n = 1,680 \)
\( \implies n = \frac{1,680 \times 100}{11.2 \times 60} = 250 \)

Step 3: Find total investment.
Market value of 250 shares = 250 × 75 = Rs. 18,750

In simple words: Each share costs Rs. 75 (face value Rs. 60 plus Rs. 15 premium). To get Rs. 1,680 dividend, Rakesh needs 250 shares. Total cost is Rs. 18,750.

📝 Teacher's Note: This question combines premium calculation and dividend calculation. Do step by step - find market price first, then number of shares, then total cost.

🎯 Exam Tip: Add premium to face value for market price. Find shares needed using dividend formula. Multiply shares by market price for total investment. Answer is Rs. 18,750.

Question 8. A man buys 400, twenty-rupee shares at a premium of Rs. 4 each and receives a dividend of 12%. Find:
(i) the amount invested by him.
(ii) his total income from the shares.
(iii) percentage return on his money.
Solution:
Given:
Nominal value of 1 share = Rs. 20
Premium = Rs. 4
Number of shares = 400
Dividend% = 12%

Step 1: Find market value and investment.
Market value of 1 share = Rs. 20 + Rs. 4 = Rs. 24
Nominal value of 400 shares = 400 × 20 = Rs. 8,000
(i) Market value of 400 shares = 400 × 24 = Rs. 9,600

Step 2: Find dividend income.
(ii) Dividend = 12% of Rs. 8,000
\( = \frac{12}{100} \times \text{Rs. } 8,000 = \text{Rs. } 960 \)

Step 3: Find percentage return.
(iii) \( \text{Percentage return} = \frac{\text{Income}}{\text{Investment}} \times 100\% \)
\( = \frac{960}{9,600} \times 100\% = 10\% \)

In simple words: He invested Rs. 9,600 to buy shares. The company gave him Rs. 960 as dividend. This means he got 10% return on his money.

📝 Teacher's Note: Percentage return is calculated on actual money spent (market value), not face value. Students often get confused between the two.

🎯 Exam Tip: Investment = Number of shares × Market price. Dividend = Dividend% × Nominal value. Return% = (Dividend ÷ Investment) × 100. Answers: (i) Rs. 9,600 (ii) Rs. 960 (iii) 10%.

Question 9. A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% on his money. Calculate:
(i) the amount invested by him.
(ii) the rate of dividend paid by the company.
Solution:
Given:
Nominal value of 1 share = Rs. 20
Discount = 20%
Number of shares = 400
Return on investment = 12%

Step 1: Find market value and investment.
Market value of 1 share = Rs. 20 - 20% of Rs. 20
= Rs. 20 - Rs. 4 = Rs. 16
(i) Investment = 400 × 16 = Rs. 6,400

Step 2: Find dividend using return percentage.
Return = 12% of Rs. 6,400 = Rs. 768
Nominal value of 400 shares = 400 × 20 = Rs. 8,000

Step 3: Find dividend percentage.
(ii) \( \text{Dividend%} = \frac{768}{8,000} \times 100\% = 9.6\% \)

In simple words: He bought shares at discount, so paid only Rs. 6,400. He got Rs. 768 as dividend (12% of his investment). This Rs. 768 is 9.6% of the total face value.

📝 Teacher's Note: When shares are at discount, market price is less than face value. Return is calculated on money actually spent, dividend percentage on face value.

🎯 Exam Tip: Find market price using discount, then total investment. Find dividend using return%, then calculate what % this is of nominal value. Answers: (i) Rs. 6,400 (ii) 9.6%.

Question 10. A company, with 10,000 shares of Rs. 100 each, declares an annual dividend of 5%.
(i) What is the total amount of dividend paid by the company?
(ii) What should be the annual income of a man who has 72 shares in the company?
(iii) If he received only 4% of his investment, find the price he paid for each share.
Answer:
Given:
Nominal value of 1 share = Rs. 100
Nominal value of 10,000 shares = 10,000 × Rs. 100 = Rs. 10,00,000

(i) Dividend% = 5%
Dividend = 5% of Rs. 10,00,000
\( = \frac{5}{100} \times 10,00,000 = \text{Rs. } 50,000 \)

(ii) Nominal value of 72 shares = Rs. 100 × 72 = Rs. 7,200
Dividend = 5% of Rs. 7,200
\( = \frac{5}{100} \times 7,200 = \text{Rs. } 360 \)

(iii) Let market value of 1 share = Rs. y
Then market value of 72 shares = Rs. (72y)
Return% = 4%
then 4% of Rs. 72y = Rs. 360
\( \implies \frac{4}{100} \times 72y = 360 \)
\( \implies y = \text{Rs. } 125 \)
In simple words: The company gives money to shareholders from its profits. We calculate how much each shareholder gets based on their shares. Then we work backwards to find the share price.

📝 Teacher's Note: Show students that dividend is always calculated on nominal value, not market value. Use a simple example like Rs. 100 note value even if you buy it for Rs. 125.

🎯 Exam Tip: Always write "Dividend = dividend% of nominal value" first. Then substitute numbers. This formula gets you marks even if calculation is wrong.

Question 11. A lady holds 1800, Rs. 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what is the return she gets as percent on her investment. Give your answer to the nearest integer.
Answer:
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 100 + 40% of Rs. 100
= Rs. 100 + Rs. 40 = Rs. 140

No. of shares purchased = 1800
Nominal value of 1800 shares = 1800 × 100 = Rs. 1,80,000
Market value of 1800 shares = 1800 × 140 = Rs. 2,52,000

(i) Dividend% = 15%
Dividend = 15% of Rs. 1,80,000
\( = \frac{15}{100} \times 1,80,000 = \text{Rs. } 27,000 \)

(ii) Return% = \( \frac{\text{Income}}{\text{Investment}} \times 100\% \)
\( = \frac{27,000}{2,52,000} \times 100\% = 10.7\% = 11\% \)
In simple words: Premium means buying above face value. The lady paid extra but still gets dividend on face value only. So her return is lower than the dividend rate.

📝 Teacher's Note: Explain premium with a movie ticket example. Face value Rs. 100 but you pay Rs. 140 (40% premium). Dividend is always on face value Rs. 100.

🎯 Exam Tip: Write return% formula first. Remember dividend is on nominal value but investment is market value paid. Round to nearest integer when asked.

Question 12. A man invests Rs. 11,200 in a company paying 6 percent per annum when its Rs. 100 shares can be bought for Rs. 140. Find:
(i) his annual dividend
(ii) his percentage return on his investment.
Answer:
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 140
Total investment = Rs. 11,200

No of shares purchased = \( \frac{11,200}{140} = 80 \text{ shares} \)
Then nominal value of 80 shares = 80 × 100 = Rs. 8,000

(i) Dividend% = 6%
Dividend = 6% of Rs. 8,000
\( = \frac{6}{100} \times 8,000 = \text{Rs. } 480 \)

(ii) Return% = \( \frac{\text{Income}}{\text{Investment}} \times 100\% \)
\( = \frac{480}{11,200} \times 100\% = 4.29\% \)
In simple words: The man buys fewer shares because each costs more than face value. But dividend is still calculated on face value only.

📝 Teacher's Note: Students often forget to find how many shares can be bought first. Make them write: Investment ÷ Market price = Number of shares.

🎯 Exam Tip: Always find number of shares first, then nominal value, then dividend. Follow this order to avoid mistakes. Show all working steps clearly.

Question 13. Mr. Sharma has 60 shares of nominal value Rs. 100 and decides to sell them when they are at a premium of 60%. He invests the proceeds in shares of nominal value Rs. 50, quoted at 4% discount, and paying 18% dividend annually. Calculate:
(i) the sale proceeds
(ii) the number of shares he buys and
(iii) his annual dividend from the shares.
Answer:
1st case (selling shares):
Nominal value of 1 share = Rs. 100
Nominal value of 60 shares = Rs. 100 × 60 = Rs. 6,000
Market value of 1 share = Rs. 100 + 60% of Rs. 100
= Rs. 100 + Rs. 60 = Rs. 160
Market value of 60 shares = Rs. 160 × 60 = Rs. 9,600

(i) Sale proceeds = Rs. 9,600

2nd case (buying new shares):
Nominal value of 1 share = Rs. 50
Market value of 1 share = Rs. 50 - 4% of Rs. 50
= Rs. 50 - Rs. 2 = Rs. 48

(ii) No of shares purchased = \( \frac{9,600}{48} = 200 \text{ shares} \)

(iii) Nominal value of 200 shares = Rs. 50 × 200 = Rs. 10,000
Dividend% = 18%
Dividend = 18% of Rs. 10,000
\( = \frac{18}{100} \times 10,000 = \text{Rs. } 1800 \)
In simple words: Mr. Sharma sold his expensive shares and bought cheaper shares. The new shares give higher dividend rate, so he gets more income.

📝 Teacher's Note: Premium means above face value, discount means below face value. Use simple examples: Rs. 100 note selling for Rs. 160 (premium) or Rs. 48 (discount).

🎯 Exam Tip: Write "1st case" and "2nd case" clearly. Find sale proceeds first, then use that money to buy new shares. Show each calculation step.

Question 14. A company with 10,000 shares of nominal value Rs. 100 declares an annual dividend of 8% to the share-holders.
(i) Calculate the total amount of dividend paid by the company.
(ii) Ramesh had bought 90 shares of the company at Rs. 150 per share. Calculate the dividend he receives and the percentage of return on his investment.
Answer:
(i) Nominal value of 1 share = Rs. 100
Nominal value of 10,000 shares = Rs. 100 × 10,000 = Rs. 10,00,000
Dividend% = 8%
Dividend = 8% of Rs. 10,00,000
\( = \frac{8}{100} \times 10,00,000 = \text{Rs. } 80,000 \)

(ii) Market value of 90 shares = Rs. 150 × 90 = Rs. 13,500
Nominal value of 90 shares = Rs. 100 × 90 = Rs. 9,000
Dividend = 8% of Rs. 9,000
\( = \frac{8}{100} \times 9,000 = \text{Rs. } 720 \)

Return% = \( \frac{\text{Income}}{\text{Investment}} \times 100\% \)
\( = \frac{720}{13,500} \times 100\% = 5\frac{1}{3}\% \)
In simple words: The company pays out total Rs. 80,000 to all shareholders. Ramesh gets his share based on how many shares he owns.

📝 Teacher's Note: Explain that total dividend depends on total nominal value of all shares. Each shareholder gets dividend based on their nominal value, not what they paid.

🎯 Exam Tip: For total dividend, multiply total nominal value by dividend%. For individual dividend, multiply individual nominal value by dividend%. Keep these separate.

Question 15. Which is the better investment: 16% Rs. 100 shares at 80 or 20% Rs. 100 shares at 120?
Answer:
1st case:
16% of Rs. 100 shares at 80 means:
Market value of 1 share = Rs. 80
Nominal value of 1 share = Rs. 100
Dividend = 16%
Income on Rs. 80 = 16% of Rs. 100 = Rs. 16
Income on Rs. 1 = \( \frac{16}{80} = \text{Rs. } 0.20 \)

2nd case:
20% of Rs. 100 shares at 120 means:
Market value of 1 share = Rs. 120
Nominal value of 1 share = Rs. 100
Dividend = 20%
Income on Rs. 120 = 20% of Rs. 100 = Rs. 20
Income on Rs. 1 = \( \frac{20}{120} = \text{Rs. } 0.17 \)

Then 16% Rs. 100 shares at 80 is better investment.
In simple words: Even though the second option gives higher dividend rate, the first option is better because you pay less for each share. You get more income per rupee invested.

📝 Teacher's Note: Teach students to always calculate income per rupee invested. Higher dividend% doesn't always mean better investment if the share price is too high.

🎯 Exam Tip: Find "Income on Re. 1" for both options. The higher value is the better investment. Write your conclusion clearly at the end.

Question 16. A man has a choice to invest in hundred-rupee shares of two firms at Rs. 120 or at Rs. 132. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum. Find:
(i) which company is giving a better return.
(ii) if a man invests Rs. 26,400 with each firm, how much will be the difference between the annual returns from the two firms.
Answer:
(i) 1st firm:
Market value of 1 share = Rs. 120
Nominal value of 1 share = Rs. 100
Dividend = 5%
Income on Rs. 120 = 5% of Rs. 100 = Rs. 5
Income on Rs. 1 = \( \frac{5}{120} = \text{Rs. } 0.041 \)

2nd firm:
Market value of 1 share = Rs. 132
Nominal value of 1 share = Rs. 100
Dividend = 6%
Income on Rs. 132 = 6% of Rs. 100 = Rs. 6
Income on Rs. 1 = \( \frac{6}{132} = \text{Rs. } 0.045 \)

Then investment in second company is giving better return.

(ii) Income on investment of Rs. 26,400 in first firm
\( = \frac{5}{120} \times 26,400 = \text{Rs. } 1,100 \)

Income on investment of Rs. 26,400 in second firm
\( = \frac{6}{132} \times 26,400 = \text{Rs. } 1,200 \)

∴ Difference between both returns = Rs. 1,200 - Rs. 1,100 = Rs. 100
In simple words: The second company gives better return per rupee invested. With the same investment amount, you get Rs. 100 more income from the second company.

📝 Teacher's Note: Show students that higher dividend% may not always mean better returns. They must consider the share price too. Always calculate per rupee return.

🎯 Exam Tip: Calculate "Income on Re. 1" first to compare. Then multiply by actual investment amount to find the difference. Show all working clearly.

Question 17. A man bought 360, ten-rupee shares of a company, paying 12% per annum. He sold the shares when their price rose to Rs. 21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at Rs. 3.50 per share. Find the annual change in his income.
Answer:
1st case:
Nominal value of 1 share = Rs. 10
Nominal value of 360 shares = Rs. 10 × 360 = Rs. 3,600
Market value of 1 share = Rs. 21
Market value of 360 shares = Rs. 21 × 360 = Rs. 7,560
Dividend% = 12%
Dividend = 12% of Rs. 3,600
\( = \frac{12}{100} \) × 3,600 = Rs. 432

2nd case:
Nominal value of 1 share = Rs. 5
Market value of 1 share = Rs. 3.50
\( \therefore \) No of shares purchased = \( \frac{7,560}{3.50} \) = 2,160 shares
Nominal value of 2160 shares = Rs. 5 × 2160 = Rs. 10,800
Dividend% = 4.5%
Dividend = 4.5% of Rs. 10,800
\( = \frac{4.5}{100} \) × 10,800 = Rs. 486

Annual change in income = Rs. 486 – Rs. 432
= Rs. 54 increase
In simple words: The man sold his old shares for more money than he paid. He used this money to buy new shares that give more dividend. So his yearly income went up by Rs. 54.

📝 Teacher's Note: Show students that when market price goes up, the person makes profit. Then this profit money can buy more shares. More shares means more dividend.

🎯 Exam Tip: Calculate both dividends separately. The difference is the change in income. Write "increase" or "decrease" clearly.

Question 18. A man sold 400 (Rs. 20) shares of a company, paying 5% at Rs. 18 and invested the proceeds in (Rs. 10) shares of another company paying 7% at Rs. 12. How many (Rs. 10) shares did he buy and what was the change in his income?
Answer:
1st case:
Nominal value of 1 share = Rs. 20
Nominal value of 400 shares = Rs. 20 × 400 = Rs. 8,000
Market value of 1 share = Rs. 18
Market value of 400 shares = Rs. 18 × 400 = Rs. 7,200
Dividend% = 5%
Dividend = 5% of Rs. 8,000
\( = \frac{5}{100} \) × 8,000 = Rs. 400

2nd case:
Nominal value of 1 share = Rs. 10
Market value of 1 share = Rs. 12
\( \therefore \) No of shares purchased = \( \frac{7,200}{12} \) = 600 shares
Nominal value of 600 shares = Rs. 10 × 600 = Rs. 6,000
Dividend% = 7%
Dividend = 7% of Rs. 6,000
\( = \frac{7}{100} \) × 6,000 = Rs. 420

Annual change in income = Rs. 420 – Rs. 400
= Rs. 20 increase
In simple words: The man bought 600 shares of the new company. His yearly income increased by Rs. 20 because the new shares give better dividend rate.

📝 Teacher's Note: Explain that dividend is always calculated on nominal value, not market value. Market value is only used to find how many shares can be bought.

🎯 Exam Tip: Always state clearly how many shares were bought and whether income increased or decreased. Write both numbers in your answer.

Question 19. Two brothers A and B invest Rs. 16,000 each in buying shares of two companies. A buys 3% hundred-rupee shares at 80 and B buys ten-rupee shares at par. If they both receive equal dividend at the end of the year, find the rate per cent of the dividend received by B.
Answer:
For A:
Total investment = Rs. 16,000
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 80
\( \therefore \) No of shares purchased = \( \frac{16,000}{80} \) = 200 shares
Nominal value of 200 shares = Rs. 100 × 200 = Rs. 20,000
Dividend% = 3%
Dividend = 3% of Rs. 20,000
\( = \frac{3}{100} \) × 20,000 = Rs. 600

For B:
Total investment = Rs. 16,000
Nominal value of 1 share = Rs. 10
Market value of 1 share = Rs. 10 (at par means nominal value = market value)
\( \therefore \) No of shares purchased = \( \frac{16,000}{10} \) = 1600 shares
Nominal value of 1600 shares = 10 × 1600 = Rs. 16,000
Dividend received by B = Dividend received by A = Rs. 600

Dividend% = \( \frac{\text{Dividend}}{\text{Nominal value}} \) × 100%
\( = \frac{600}{16,000} \) × 100%
= 3.75%
In simple words: B's dividend rate is 3.75%. Even though both brothers get the same dividend amount (Rs. 600), their rates are different because they bought different types of shares.

📝 Teacher's Note: "At par" means market price equals nominal price. Students often forget this. Also explain that equal dividend amount does not mean equal dividend rate.

🎯 Exam Tip: When dividend amounts are equal, use the formula: Dividend% = (Dividend ÷ Nominal value) × 100. Always write the percentage symbol.

Question 20. A man invests Rs. 20,020 in buying shares of nominal value Rs. 26 at 10% premium. The dividend on the shares is 15% per annum. Calculate:
(i) the number of shares he buys.
(ii) the dividend he receives annually.
(iii) the rate of interest he gets on his money.
Answer:
Total investment = Rs. 20,020
Nominal value of 1 share = Rs. 26
Market value of 1 share = Rs. 26 + 10% of Rs. 26
= Rs. 26 + Rs. 2.60 = Rs. 28.60

(i) No of shares purchased = \( \frac{20,020}{28.60} \) = 700 shares

Nominal value of 700 shares = Rs. 26 × 700 = Rs. 18,200
Dividend% = 15%

(ii) Dividend = 15% of Rs. 18,200
\( = \frac{15}{100} \) × 18,200 = Rs. 2,730

(iii) Income% = \( \frac{\text{Income}}{\text{Investment}} \) × 100%
\( = \frac{2,730}{20,020} \) × 100% = \( \frac{150}{11} \)% = \( 13\frac{7}{11} \)%
In simple words: He bought 700 shares. He gets Rs. 2,730 as dividend every year. His return rate on the money he invested is about 13.6%.

📝 Teacher's Note: Premium means paying extra. 10% premium on Rs. 26 means paying Rs. 2.60 extra, so total Rs. 28.60. Rate of interest is calculated on actual money invested, not nominal value.

🎯 Exam Tip: For part (iii), use actual investment amount in the denominator, not nominal value. Write the fraction form if division doesn't give a clean decimal.

Exercise 3C

Question 1. By investing Rs. 45,000 in 10% Rs. 100 shares, Sharad gets Rs. 3,000 as dividend. Find the market value of each share.
Answer:
Annual income from 1 share = 10% of Rs. 100 = Rs. 10
Total annual income = Rs. 3000
\( \therefore \) Number of shares bought = \( \frac{\text{Total annual income}}{\text{Annual income from 1 share}} = \frac{3000}{10} \) = 300
\( \Rightarrow \) Market value of one share = \( \frac{\text{Total investment}}{\text{Number of shares}} = \frac{45000}{300} \) = Rs. 150
In simple words: Each share gives Rs. 10 dividend. To get Rs. 3000 total, he must have 300 shares. So each share cost Rs. 150 in the market.

📝 Teacher's Note: Start with dividend per share, then find total shares, then find market price per share. This step-by-step method prevents mistakes.

🎯 Exam Tip: Write all three steps clearly: dividend per share, number of shares, then market value per share. Show your division work.

Question 2. Mrs. Kulkarni invests Rs. 1,31,040 in buying Rs. 100 shares at a discount of 9%. She sells shares worth Rs.72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss on the whole.
Answer:
Investment = Rs. 131040
N.V. of 1 share = Rs. 100
Discount = 9% of Rs. 100 = Rs. 9
\( \therefore \) M.V. of 1 share = Rs. 100 - Rs. 9 = Rs. 91
\( \therefore \) Number of shares purchased = \( \frac{\text{Investment}}{\text{M.V. of 1 share}} = \frac{131040}{91} \) = 1440

Number of shares worth Rs. 72000 = \( \frac{72000}{100} \) = 720
\( \therefore \) Mrs. Kulkarni sells 720 shares at a premium of 10%
M.V. of 1 share = Rs.100 + Rs. 10 = Rs. 110
\( \therefore \) Selling price of 720 shares = 720 × Rs. 110 = Rs. 79200
Number of remaining shares = 1440 - 720 = 720
She sells 720 shares at a discount of 5%
M.V. of 1 share = Rs. 100 - Rs. 5 = Rs. 95
\( \therefore \) Selling price of 720 shares = 720 × Rs. 95 = Rs. 68400
\( \therefore \) Total selling price = Rs. (79200 + 68400) = Rs. 147600
\( \therefore \) Total gain = Total selling price - Total investment
= Rs. (147600 - 131040)
= Rs. 16560
In simple words: She bought 1440 shares for Rs. 131040. She sold them for Rs. 147600 total. Her profit is Rs. 16560.

📝 Teacher's Note: Break this into steps: find total shares bought, then calculate selling price for each batch separately, then find total gain. Students often mix up the different selling prices.

🎯 Exam Tip: Calculate selling price for each group of shares separately. Add them to get total selling price. Then subtract total investment to find gain or loss.

Question 3. A man invests a certain sum on buying 15% Rs. 100 shares at 20% premium. Find:
(i) His income from one share
(ii) The number of shares bought to have an income, from the dividend, Rs. 6480
(iii) Sum invested
Answer:
(i) Dividend on one share = 15% of Rs. 100
= Rs. \( \left(\frac{15}{100} \times 100\right) \)
= Rs. 15
So, the income from one share is Rs. 15.

(ii) Number of shares bought by the man
= \( \frac{\text{annual income}}{\text{dividend on one share}} \)
= \( \frac{6480}{15} \)
= Rs. 432

(iii) Since the man bought shares of Rs. 100 at 20% premium, the market value of one share
= Rs. \( \left(1 + \frac{20}{100}\right) \times 100 \)
= Rs. \( \left(\frac{120}{100} \times 100\right) \)
= Rs. 120
\( \therefore \) His total investment = number of shares × market value of one share
= 432 × 120
= Rs. 51,840
In simple words: Each share gives Rs. 15 dividend. To get Rs. 6480, he needs 432 shares. Each share costs Rs. 120, so total investment is Rs. 51,840.

📝 Teacher's Note: Premium means extra cost. 20% premium on Rs. 100 means paying Rs. 120. Always calculate market value first, then find total investment.

🎯 Exam Tip: For part (ii), divide total dividend by dividend per share. For part (iii), multiply number of shares by market value per share (not nominal value).

Question 4. Gagan invested 80% of his savings in 10% Rs. 100 shares at 20% premium and the rest of his savings in 20% Rs. 50 shares at 20% discount. If his incomes from these shares is
Answer:
Note: The question appears to be incomplete in the source material.

📝 Teacher's Note: When a question is incomplete, read it carefully and identify what information is missing. In exams, such questions are usually printing errors.

🎯 Exam Tip: If you find an incomplete question in an exam, inform the teacher immediately. Don't waste time trying to solve incomplete problems.

Question. Rs. 5,600 calculate:
(i) His investment in shares on the whole
(ii) The number of shares of first kind that he bought
(iii) Percentage return, on the shares bought on the whole.
Answer:
(i) Let the total savings be Rs. x.

For 1st part:
N.V. of each share = Rs. 100
M.V. of each share = 100 + \( \frac{20}{100} \)(100) = Rs. 120
Number of shares bought = \( \frac{0.8x}{120} \) ...(Investment = Rs. x)
Dividend on each share = 10% of 100 = Rs. 10 ...(Rate = 10%)
Total dividend = 10 × \( \frac{0.8x}{120} \) = Rs. \( \frac{0.8x}{12} \)

For 2nd part:
N.V. of each share = Rs. 50
M.V. of each share = 50 - \( \frac{20}{100} \)(50) = Rs. 40
Number of shares bought = \( \frac{0.2x}{40} \) ...(Investment = Rs. x)
Dividend on each share = 20% of 50 = Rs. 10 ...(Rate = 20%)
Total dividend = 10 × \( \frac{0.2x}{40} \) = \( \frac{0.2x}{4} \)

Given that dividends from both investments are Rs. 5600:
\( \frac{0.8x}{12} + \frac{0.2x}{4} = 5600 \)
\( \frac{0.8x + 0.6x}{12} = 5600 \)
\( x = \frac{5600 × 12}{1.4} \)
\( x = 48,000 \)

Thus, his investment in shares on the whole is Rs. 48,000.

(ii) Number of shares bought = \( \frac{0.8x}{120} = \frac{0.8 × 48,000}{120} \) = Rs. 320

(iii) Total dividend (return) = \( \frac{0.8x}{12} + \frac{0.2x}{4} \)
= \( \frac{0.8(48,000)}{12} + \frac{0.2(48,000)}{4} \)
= 0.8 × 4,000 + 0.2 × 12,000
= Rs. 5600

Percentage return = \( \frac{5600}{48,000} × 100 = 11\frac{2}{3}% \)

In simple words: The person split his money into two parts. He bought two types of shares. First type was expensive but gave less dividend. Second type was cheap but gave more dividend. Together both gave him Rs. 5,600 as income.

📝 Teacher's Note: Show students that dividend is calculated on face value (N.V.), not market value (M.V.). This is a common mistake. Use simple examples like a Rs. 100 share bought at Rs. 120 still gives 10% of Rs. 100 = Rs. 10 dividend.

🎯 Exam Tip: Always write "Given" first, then list all values clearly. Show each step separately. Write the final answers with proper units. You get marks for method even if calculation is wrong.

Question 5. Ashwarya bought 496, Rs. 100 shares at Rs. 132 each, find:
(i) Investment made by her
(ii) Income of Ashwarya from these shares, if the rate of dividend is 7.5%.
(iii) How much extra must ashwarya invest in order to increase her income by Rs. 7,200.
Answer:
(i) N.V. of each share = Rs. 100
M.V. of each share = Rs. 132
Investment made by her = 496 × 132 = Rs. 65,472

(ii) Dividend on 1 share = 7.5% of Rs. 100 = Rs. 7.5
So, income of Ashwarya from these shares = 496 × 7.5 = Rs. 3,720

(iii) If she wants to increase her income by Rs. 7,200,
the number of shares she should buy = \( \frac{\text{increase in the income}}{\text{income of one share}} = \frac{7,200}{7.5} \) = Rs. 960
So, she should invest = 960 × 7.5 = Rs. 1,26,720

In simple words: Ashwarya bought shares and gets regular income from them. To get more income, she needs to buy more shares of the same type.

📝 Teacher's Note: Explain that dividend rate is always on face value, not market value. Use the analogy of rent on a house - the rent depends on the house value, not what you paid for it.

🎯 Exam Tip: Write clearly: "Investment = Number of shares × Market Value" and "Income = Number of shares × Dividend per share". These formulas get you marks.

Question. A company pays a dividend of 15% on its Rs. 100 shares from which income tax at the rate of 20% is deducted. Find:
(i) The net annual income of Gopal who owns 7,200 shares of this company
(ii) The sum invested by Ramesh when the shares of this company are bought by him at 20% premium and the gain required by him(after deduction of income tax) is Rs. 9,000
Answer:
(i) Let the number of shares be x.
Annual income = Rate of dividend × Nominal Value × Number of shares
= \( \frac{15}{100} × 100 × x \)
= 15x ......(i)
Since the income tax is given to be 20% which is deducted,
15x - 20% of 15x = 15x - \( \frac{20}{100} \)(15x) = 15x - 3x = 12x
Thus, the net annual income of Gopal who owns 7,200 shares of this company
= 12x
= 12(7,200)
= Rs. 86,400

(ii) Let the sum invested by him be Rs. S.
N.V. of each share = Rs. 100
M.V. of each share = Rs. 100 + 20% of Rs. 100 = Rs. 120
Number of each share = Rs. \( \frac{S}{120} \)
Dividend on each share = Rs. 15% of Rs. 100 = Rs. 15
Total dividend = Rs. 15 × \( \frac{S}{120} = \frac{S}{8} \)
Since the income tax is given to be 20% which is deducted,
The gain = \( \frac{S}{8} - \frac{20}{100}(\frac{S}{8}) = \frac{S}{8} - \frac{S}{40} = \frac{S}{10} \)
Given the gain required by him is Rs. 9000.
So, \( \frac{S}{10} = 9000 \)
⇒ S = Rs. 90,000
Hence, the sum invested by Ramesh is Rs. 90,000.

In simple words: The company gives 15% dividend but the government takes 20% tax from it. So net income is less. Think of it like getting Rs. 15 but giving Rs. 3 as tax, so you keep Rs. 12.

📝 Teacher's Note: Use real examples of income tax. If a student gets Rs. 100 as pocket money and parents take Rs. 20 as saving, the student keeps Rs. 80. Same logic applies here.

🎯 Exam Tip: Always calculate net income = Gross income - Tax. Write this formula clearly. Also show that dividend is calculated on face value, not market value.

Question. Mr. Joseph sold some Rs. 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in Rs. 100 shares paying 16% dividend at a discount of 20%. By doing so, his income was increased by Rs. 4,800. Find the number of shares originally held by Mr. Joseph.
Answer:
Let the number of shares be x.
Annual income = Rate of dividend × Nominal Value × Number of shares
= \( \frac{10}{100} × 100 × x \)
= 10x ......(i)
Since each share is sold at a discount of 25%,
selling price of one share = Rs. 100 - \( \frac{25}{100} \) = Rs.75
So, selling price of x shares = Rs. 75x
The proceeds = the new investment = Rs. 75x
Here the N.V. = Rs. 100
M.V. of each share = Rs. 80
Rate of dividend = 16%
Number of shares = \( \frac{75x}{80} \)
Annual income = Rate of dividend × Nominal Value × Number of shares
= \( \frac{16}{100} × 100 × \frac{75x}{80} \)
= 15x ......(ii)
From (i) and (ii), we get
15x - 10x = 4800
⇒ 5x = 4800
⇒ x = 960
So, the number of shares originally were 960.

In simple words: Mr. Joseph sold his old shares and bought new shares with the same money. The new shares gave him more income than the old shares. The difference in income was Rs. 4,800.

📝 Teacher's Note: Explain discount and premium clearly. Discount means selling below face value. Premium means selling above face value. Use simple shopping examples like sale price vs. marked price.

🎯 Exam Tip: Write the income formula for both old and new shares separately. Then find the difference. This step-by-step method gets you full marks even if you make small calculation errors.

Question 6. Gopal has some Rs. 100 shares of company A, paying 10% dividend. He sells a certain number of these shares at a discount of 20% and invests the proceeds in Rs. 100 shares at Rs. 60 of company B paying 20% dividend. If his income, from the shares sold, increases by Rs. 18,000, find the number of shares sold by Gopal.
Answer:
Let the number of shares the man sold be x.
N.V. of share = Rs.100
Rate of dividend = 10%
Dividend on each share = 10% of Rs. 100 = Rs.10
So, the dividend on x shares = Rs. 10 × x = Rs. 10x
Selling price of each share = Rs.100 - 20% of Rs. 100 = Rs. 80
Amount obtained on selling x shares = Rs. 80 × x = Rs. 80x
The proceeds he invested in Rs. 100 shares at Rs. 60 of company B paying 20% dividend.
N.V. of share = Rs.100
M.V. of each share = Rs. 60 = Rs. 60
Number of shares bought by the man = \( \frac{\text{Amount invested}}{\text{M.V. of each share}} \)
= \( \frac{80x}{60} \)
= \( \frac{4x}{3} \)
Dividend on each share = 20% of Rs. 100 = Rs. 20
Total dividend received = Dividend on each share × Number of shares
= 20 × \( \frac{4x}{3} \)
= \( \frac{80x}{3} \)
Increase in the income = Rs. 18,000
⇒ \( \frac{80x}{3} - 10x = 18,000 \)
⇒ \( \frac{50x}{3} = 18,000 \)
x = Rs. 1080
Hence, the number of shares sold by Gopal is Rs. 1080.

In simple words: Gopal sold some shares from company A and bought shares from company B with that money. Company B shares gave him more dividend per share, so his total income increased.

📝 Teacher's Note: Draw a simple diagram showing money flow: Sell shares → Get money → Buy new shares → Get more income. This visual helps students understand the process clearly.

🎯 Exam Tip: Set up two income calculations: old income and new income. Then write: New income - Old income = Given increase. This format always works and gets you marks.

Question 7. A man invests a certain sum of money in 6% hundred-rupee shares at Rs. 12 premium. When the shares fell to Rs. 96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at Rs. 8. If the change in his income is Rs. 540, Find the sum
Answer:
[Note: This appears to be an incomplete question as the solution is not provided in the source material.]

In simple words: The man bought shares when they were expensive, then sold them when price fell. He used that money to buy different shares that gave him more dividend income.

📝 Teacher's Note: This question involves buying at premium (above face value) and selling at discount (below face value). Make sure students understand these terms clearly before solving.

🎯 Exam Tip: Calculate the loss on selling first, then find the new investment amount. Then compare old income with new income to get the change. Show all steps clearly.

Question 8. Mr. Gupta has a choice to invest in ten-rupee shares of two firms at Rs. 13 or at Rs. 16. If the first firm pays 5% dividend and the second firm pays 6% dividend per annum, find:
(i) which firm is paying better.
(ii) if Mr. Gupta invests equally in both the firms and the difference between the returns from them is Rs. 30, find how much, in all, does he invest.
Answer:
(i) 1st firm
Nominal value of 1 share = Rs. 10
Market value of 1 share = Rs. 13
Dividend% = 5%
Dividend = 5% of Rs. 10 = Rs. 0.50

\( \text{Income%} = \frac{\text{Income}}{\text{Investment}} \times 100\% \)

\( = \frac{0.50}{13} \times 100\% = 3.846\% \)

2nd firm
Nominal value of 1 share = Rs. 10
Market value of 1 share = Rs. 16
Dividend% = 6%
Dividend = 6% of Rs. 10 = Rs. 0.60

\( \text{Income%} = \frac{\text{Income}}{\text{Investment}} \times 100\% \)

\( = \frac{0.60}{16} \times 100\% = 3.75\% \)

Then first firm is paying better than second firm.

(ii) Let money invested in each firm = Rs. y

For 1st firm
No. of shares purchased = \( \frac{y}{13} \) shares

Total dividend = Rs. 0.50 × \( \frac{y}{13} \) = Rs. \( \frac{y}{26} \)

For 2nd firm
No. of shares purchased = \( \frac{y}{16} \) shares

Total dividend = Rs. 0.60 × \( \frac{y}{16} \) = Rs. \( \frac{3y}{80} \)

Given- difference of both dividend = Rs. 30

\( \implies \frac{y}{26} - \frac{3y}{80} = \text{Rs. 30} \)

\( \implies \frac{y}{1040} = \text{Rs. 30} \)

\( \implies y = \text{Rs. 30} \times 1040 = \text{Rs. 31,200} \)

Total money invested in both firms = Rs. 31,200 × 2 = Rs. 62,400
In simple words: We compare the returns by dividing dividend by the price we pay. First firm gives better returns. For part 2, we set up equations to find equal investment amounts.

📝 Teacher's Note: Show students how to calculate percentage return. Many students forget to divide by market price, not face value. Use simple examples like bank interest rates.

🎯 Exam Tip: Always compare income percentage, not just dividend amount. Write "first firm is better" clearly. Show all working for the equation in part (ii).

Question 9. Ashok invested Rs. 26,400 in 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475, find the:
(i) number of shares he bought.
(ii) market value of each share.
Answer:
(i) Total dividend = Rs. 2,475

And, dividend on each share = 12% of Rs. 25 = \( \frac{12}{100} \times \text{Rs. 25} = \text{Rs. 3} \)

Number of shares bought = \( \frac{\text{Total dividend}}{\text{Dividend on 1 share}} = \frac{2475}{3} = 825 \)

(ii) Market value of 825 shares = Rs. 26,400

Market value of each share = \( \frac{\text{Total investment}}{\text{No. of shares}} = \frac{26400}{825} = \text{Rs. 32} \)
In simple words: First find how much dividend one share gives. Then divide total dividend by this to get number of shares. Market value is total money divided by number of shares.

📝 Teacher's Note: Students often confuse face value and market value. Face value is Rs. 25, but he pays Rs. 32 per share. Dividend is always on face value.

🎯 Exam Tip: Write dividend calculation clearly. Always use face value for dividend, not market value. Show division steps for marks.

Question 10. A man invested Rs. 45,000 in 15% Rs100shares quoted at Rs. 125. When the market value of these shares rose to Rs. 140, he sold some shares, just enough to raise Rs. 8,400. Calculate:
(i) the number of shares he still holds;
(ii) the dividend due to him on these remaining shares.
Answer:
(i) Total investment = Rs. 45,000
Market value of 1 share = Rs. 125

No of shares purchased = \( \frac{45,000}{125} \) = 360 shares

Nominal value of 360 shares = Rs. 100 × 360 = Rs. 36,000

Let no. of shares sold = n
Then sale price of 1 share = Rs. 140
Total sale price of n shares = Rs. 8,400

Then n = \( \frac{8,400}{140} \) = 60 shares

The no. of shares he still holds = 360 – 60 = 300

(ii) Nominal value of 300 shares = Rs. 100 × 300 = Rs. 30,000
Dividend% = 15%
Dividend = 15% of Rs. 30,000
= \( \frac{15}{100} \times 30,000 = \text{Rs. 4,500} \)
In simple words: He bought 360 shares originally. He sold 60 shares to get Rs. 8,400. So he has 300 shares left. Dividend is 15% of face value of remaining shares.

📝 Teacher's Note: Students forget that selling price is different from buying price. Market value changed from Rs. 125 to Rs. 140. This is why he could sell fewer shares to get Rs. 8,400.

🎯 Exam Tip: Calculate shares sold by dividing money raised by new market price. Always find dividend on remaining shares, not all shares. Show each step clearly.

Question 11. Mr.Tiwari. invested Rs. 29,040 in 15% Rs100 shares quoted at a premium of 20%. Calculate:
(i) the number of shares bought by Mr. Tiwari.
(ii) Mr. Tiwari's income from the investment.
(iii) the percentage return on his investment.
Answer:
Total investment = Rs. 29,040
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 100+ 20% of Rs. 100
= Rs. 100 + Rs. 20 = Rs. 120

No of shares purchased = \( \frac{29,040}{120} \) = 242 shares

Nominal value of 242 shares = Rs. 100 x 242 = Rs. 24,200
Dividend% = 15%
Dividend = 15% of Rs. 24,200
= \( \frac{15}{100} \times 24,200 = \text{Rs. 3,630} \)

\( \text{Income%} = \frac{\text{Income}}{\text{Investment}} \times 100\% \)

= \( \frac{3,630}{29,040} \times 100\% \)

= 12.5%
In simple words: Premium means paying more than face value. 20% premium on Rs. 100 means paying Rs. 120. Income percentage is yearly dividend divided by money invested.

📝 Teacher's Note: Premium means extra money above face value. Students often confuse this. Use examples like buying train tickets at higher prices during festivals.

🎯 Exam Tip: Premium of 20% on Rs. 100 = Rs. 100 + Rs. 20 = Rs. 120. Always calculate income percentage for comparison. Write formula first, then substitute.

Question 12. A dividend of 12% was declared on Rs. 150 shares selling at a certain price. If the rate of return is 10%, calculate:
(i) the market value of the shares.
(ii) the amount to be invested to obtain an annual dividend of Rs. 1,350.
Answer:
(i)Nominal value of 1 share= Rs150
Dividend%= 12%
Dividend on I share= 12% of Rs150
= \( \frac{12}{100} \times \text{Rs150} = \text{Rs18} \)

Let market value of 1 share= Rs y
Return%= 10%
10% of Rs(y) =Rs 18
= \( \frac{10}{100} \times y = \text{Rs 18} \)
⟹ y = Rs 180

(ii)when dividend is Rs 18, then investment is Rs180
When dividend is Rs1,350, then investment
= \( \frac{180}{18} \times \text{Rs1,350} \)
= Rs 13,500
In simple words: Rate of return means how much profit you get compared to money invested. We use this to find market price. Then we use proportion to find bigger investment.

📝 Teacher's Note: Rate of return is like bank interest rate. If you want 10% return and dividend is Rs. 18, you should pay Rs. 180 for that share.

🎯 Exam Tip: Set up equation: (Dividend/Market Price) × 100 = Rate of return. Solve for market price. Use proportions for part (ii).

Question 13. Divide Rs. 50,760 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 100 shares at 8% premium, the annual incomes from both the investments are equal.
Answer:
Total investment= Rs50,760
Let 1st part= Rs y
2nd part= Rs(50,760-y)

For 1st part
Nominal value of 1 share= Rs100
Market value of 1 share= Rs100 - 8% of Rs100
= Rs100 - Rs8= Rs92

No. of shares purchased= \( \frac{y}{92} \) shares

Dividend%= 8%
Dividend on 1 share= 8% of Rs100= Rs8

Total dividend= \( \frac{y}{92} \times \text{Rs8} = \text{Rs}\frac{2y}{23} \)
In simple words: We need to split Rs. 50,760 so both investments give same yearly income. Discount means paying less than face value. Premium means paying more.

📝 Teacher's Note: Discount of 8% on Rs. 100 means paying Rs. 92. Premium of 8% means paying Rs. 108. Set up equations for equal incomes and solve.

🎯 Exam Tip: Let first part be y, second part be (50,760-y). Set up income equations and make them equal. Solve for y to get the division.

Question 14. Mr. Shameem invested \( 33\frac{1}{3}\% \) of his savings in 20% Rs. 50 shares quoted at Rs. 60 and the remainder of the savings in 10% Rs. 100 share quoted at Rs. 110. If his total income from these investments is Rs. 9,200; find:
(i) his total savings
(ii) the number of Rs. 50 share
(iii) the number of Rs. 100 share.
Answer:
Let his total savings = Rs. y
1st case:
His savings = \( 33\frac{1}{3}\% \) of y = Rs. \( \frac{y}{3} \)
Market price of 1 share = Rs. 60
Then shares purchased = \( \frac{y}{3 \times 60} = \frac{y}{180} \)
Dividend on 1 share = 20% of Rs. 50 = Rs. 10
Total dividend = \( \frac{y}{180} \times 10 = Rs. \frac{y}{18} \)

2nd case:
His saving = \( 66\frac{2}{3}\% \) of y = Rs. \( \frac{2y}{3} \)
Market price of 1 share = Rs. 110
Then shares purchased = \( \frac{2y}{3 \times 110} = \frac{y}{165} \)
Dividend on 1 share = 10% of Rs. 100 = Rs. 10
Total dividend = \( \frac{y}{165} \times 10 = Rs. \frac{2y}{33} \)

According to question:
Total income = Rs. 9,200
\( \frac{y}{18} + \frac{2y}{33} = Rs. 9,200 \)
\( \frac{23y}{198} = Rs. 9,200 \)
\( y = \frac{9,200 \times 198}{23} = Rs. 79,200 \) Ans.

The number of Rs. 50 share = \( \frac{79,200}{180} = 440 \) Ans.
The number of Rs. 100 share = \( \frac{79,200}{165} = 480 \) Ans.
In simple words: We found out his total savings by adding the dividends from both types of shares. Then we used this total to find how many shares of each type he bought.

📝 Teacher's Note: Show students that total savings equals first investment plus second investment. A common mistake is forgetting to convert mixed fractions to improper fractions.

🎯 Exam Tip: Always write "Let total savings = y" first. Show all steps clearly. Check that your answer makes sense by adding the two parts of investment.

Question 15. Vivek invests Rs. 4,500 in 8%, Rs. 10 shares at Rs. 15. He sells the shares when the price rises to Rs. 30, and invests the proceeds in 12% Rs. 100 shares at Rs. 125. Calculate:
(i) the sale proceeds
(ii) the number of Rs. 125 shares he buys
(iii) the change in his annual income from dividend.
Answer:
1st case:
Total investment = Rs. 4,500
Market value of 1 share = Rs. 15
∴ No of shares purchased = \( \frac{4,500}{15} \) = 300 shares
Nominal value of 1 share = Rs. 10
Nominal value of 300 shares = Rs. 10 × 300 = Rs. 3,000
Dividend = 8% of Rs. 3,000
= \( \frac{8}{100} \) × 3,000 = Rs. 240
Sale price of 1 share = Rs. 30
Total sale price = Rs. 30 × 300 = Rs. 9,000

(ii) New market price of 1 share = Rs. 125
∴ No of shares purchased = \( \frac{9,000}{125} \) = 72 shares

(iii) New nominal value of 1 share = Rs. 100
New nominal value of 72 shares = Rs. 100 × 72 = Rs. 7,200
Dividend% = 12%
New dividend = 12% of Rs. 7,200
= \( \frac{12}{100} \) × 7,200 = Rs. 864
Change in annual income = Rs. 864 – Rs. 240 = Rs. 624
In simple words: Vivek made money by selling shares at a higher price. Then he bought different shares that gave him more dividend money each year.

📝 Teacher's Note: Explain that market price changes but nominal value stays the same. Dividend is always calculated on nominal value, not market value.

🎯 Exam Tip: For sale proceeds, multiply number of shares by selling price. For dividend change, subtract old dividend from new dividend. Show all calculations step by step.

Question 16. Mr.Parekh invested Rs. 52,000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year he sells the shares at a premium of Rs. 20. Find:
(i) The annual dividend
(ii) The profit earned including his dividend.
Answer:
Rate of dividend = 8%
Investment = Rs. 52000
Market Rate = Rs. 100 – 20 = Rs. 80
No. of shares purchased = \( \frac{52000}{80} \) = 650

(i) Annual dividend = 650 × 8 = Rs. 5200

(ii) On selling, market rate = Rs. 100 + 20 = Rs. 120
⇒ Sale price = 650 × 120 = Rs. 78000
Profit = Rs. 78000 – Rs. 52000 = Rs. 26000
⇒ Total gain = 26000 + 5200 = Rs. 31200
In simple words: Mr. Parekh bought shares cheap and sold them expensive. He also got dividend money. So his total profit includes both the selling profit and the dividend.

📝 Teacher's Note: Teach students that "discount" means buying below face value and "premium" means above face value. Dividend is calculated on face value × rate × number of shares.

🎯 Exam Tip: Total gain = Capital gain + Dividend received. Write both parts separately then add them. Don't forget to include the dividend in final answer.

Question 17. Salman buys 50 shares of face value Rs. 100 available at Rs. 132.
(i) What is his investment?
(ii) If the dividend is 7.5%, what will be his annual income?
(iii) If he wants to increase his annual income by Rs. 150, how many extra shares should he buy?
Answer:
Number of shares bought = 50
N.V. of one share = Rs. 100
M.V. of each share = Rs. 132
(i) Investment = M.V. of each share × Number of shares
= Rs. 132 × 50
= Rs. 6600

(ii) Since dividend on 1 share = 7.5% of N.V. = \( \frac{7.5}{100} \) × 100 = Rs. 7.50
His annual income = Rs. 7.50 × 50 = Rs. 375

(iii) Extra shares to be bought = \( \frac{\text{Increase in annual income}}{\text{Income in one share}} = \frac{150}{7.50} \) = 20
In simple words: Investment means how much money you pay to buy shares. Annual income is the dividend money you get every year. To get more income, you need to buy more shares.

📝 Teacher's Note: Remind students that investment is always at market value but dividend is calculated on nominal (face) value. Use simple division to find extra shares needed.

🎯 Exam Tip: Investment = Market value × Number of shares. Annual income = Dividend per share × Number of shares. For extra shares, divide required extra income by income per share.

Question 18. Salman invests a sum of money in Rs. 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is Rs. 600, calculate:
(i) The number of shares he bought
(ii) His total investment
(iii) The rate of return on his investment.
Answer:
N.V. of each share = Rs. 50
M.V. of each share = Rs. 50 + 20% of Rs. 50
= 50 + \( \frac{20}{100} \) × 50
= 50 + 10
= Rs. 60

Dividend on one share = 15% of Rs. 50 = \( \frac{15}{100} \) × 50 = 7.5

(i) Number of shares bought = \( \frac{\text{Total dividend}}{\text{Dividend on one share}} = \frac{600}{7.5} \) = 80

(ii) His total investment = Number of shares × M.V. of one share
= 80 × Rs. 60
= Rs. 4800

(iii) Rate of return = \( \frac{\text{Total dividend}}{\text{Total investment}} \times 100\% = \frac{600}{4800} \times 100\% \) = 12.5%
In simple words: First find dividend per share. Then divide total dividend by this to get number of shares. Rate of return shows how much profit you get for every 100 rupees you invest.

📝 Teacher's Note: Explain that 20% premium means market price is 120% of face value. Rate of return compares yearly income with money invested - like interest rate in a bank.

🎯 Exam Tip: For number of shares, divide total dividend by dividend per share. Rate of return = (Annual dividend ÷ Investment) × 100. Always show percentage sign in final answer.

Question 19. Rohit invested Rs. 9,600 on Rs. 100 shares at Rs. 20 premium paying 8% dividend. Rohit sold the shares when the price rose to Rs. 160. He invested the proceeds (excluding dividend) in 10% Rs. 50 shares at Rs. 40. Find the:
(i) Original number of shares
(ii) Sale proceeds
(iii) New number of shares
(iv) Change in the two dividends.
Answer:
(i) 100 shares at Rs. 20 premium means
Nominal value of the share is Rs. 100
and its market value = 100 + 20 = Rs. 120
Money required to buy 1 share = Rs. 120
∴ Number of shares = \( \frac{\text{Money Invested}}{\text{Market Value of 1 Share}} = \frac{9600}{120} \) = 80

(ii) Each share is sold at Rs. 160
∴ Sale Proceeds = 80 × Rs. 160 = Rs. 12,800

(iii) Now, investment = Rs. 12800
Dividend = 10%
Net Value = 50
Market Value = Rs. 40
∴ Number of shares = \( \frac{\text{Investment}}{\text{Market Value}} = \frac{12800}{40} \) = 320

(iv) Now, dividend on 1 share = 10% of N.V. = 10% of 50 = 5
⇒ Dividend on 320 shares = 320 × 5 = 1600
Thus, change in two dividends = 1600 – 640 = 960
In simple words: Rohit sold his expensive shares and bought cheaper ones. The new shares gave him much more dividend money because he could buy many more shares with the same money.

📝 Teacher's Note: Show students that selling at higher price gives more money to reinvest. Buying shares at lower market price means you can buy more shares, so more dividend.

🎯 Exam Tip: For original shares, divide investment by market price. For new dividend, calculate dividend per share first, then multiply by number of shares. Change = New dividend - Old dividend.

Question 20. How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.
Answer:
Given:
Face value of each share = Rs. 50
Market price of each share = Rs. 60
Dividend rate = 10%
Required income = Rs. 450

Step 1: Find dividend per share.
Dividend on 1 share = \( \frac{10}{100} \times 50 = \text{Rs. 5} \)

Step 2: Find number of shares required.
Number of shares bought = \( \frac{\text{Total dividend}}{\text{Dividend per share}} = \frac{450}{5} = 90 \)

Step 3: Find total investment.
Total investment = 90 × 60 = Rs. 5400

Step 4: Find yield percentage.
Percentage return = \( \frac{\text{Total dividend}}{\text{Total investment}} \times 100 = \frac{450}{5400} \times 100 = 8.33 \approx 8\% \)

Therefore:
Total investment = Rs. 5400
Yield percent = 8%
In simple words: The man needs to buy 90 shares at Rs. 60 each to get Rs. 450 income. His total investment is Rs. 5400. His return rate is 8% of what he invested.

📝 Teacher's Note: Explain that dividend is always calculated on face value, not market price. Show students that yield is the actual return on money invested. Use simple examples like bank interest to make it clear.

🎯 Exam Tip: Always write "dividend = dividend rate × face value" first. Calculate number of shares needed, then total investment. Remember yield = (dividend income ÷ total investment) × 100. Round to nearest whole number as asked.