OP Malhotra Class 10 Maths Solutions Chapter 3 Shares and Dividends Exercise 3 (B)

Question 1. Find the number of shares that can be bought and the income obtained by investing :
(a) Rs. 50 in (Re. 1) shares at Rs. 1.25 paying 8%.
(b) Rs. 240 in (Rs. 5) shares at Rs. 8, paying 9%.
Answer:
(a) Investment = Rs. 50
Face value of share = Re. 1
Market value = Rs. 1.25
Rate of dividend = 8%
Number of shares \( = \frac { 50 }{ 1.25 } = \frac{50 \times 100}{125} = 40 \) shares
Face value of 40 shares \( = 40 \times \text{Re. } 1 = \text{Rs. } 40 \)
Amount of dividend \( = \text{Rs. } \frac { 40 \times 8 }{ 100 } = \text{Rs. } 3.20 \)
(b) Investment = Rs. 240
Face value of each share = Rs. 5
Market value = Rs. 8
Rate of dividend = 9%
Number of shares \( = \text{Rs. } \frac { 240 }{ 8 } = 30 \)
Face value of 30 shares \( = 30 \times 5 = \text{Rs. } 150 \)
Amount of dividend \( = \text{Rs. } \frac{150 \times 9}{100} \)
\( = \text{Rs. } \frac { 1350 }{ 100 } = \text{Rs. } 13.50 \)
In simple words: To find the number of shares, divide the total investment by the market value of one share. The income (dividend) is calculated on the face value of the shares using the given dividend rate.

🎯 Exam Tip: Remember that dividend is always calculated on the face value (or nominal value) of the shares, not the market value or investment amount.

Question 2. A man bought 160 (Rs. 5) shares for Rs. 360. At what price did the shares stand? At what premium or discount were they quoted?
Answer:
Number of shares = 160
Face value of each share = Rs. 5
Amount paid for 160 shares = Rs. 360
Market value of each share \( = \text{Rs. }\frac {360}{160} = \text{Rs. } \frac {9}{4} = \text{Rs. } 2.25 \)
Difference between face value and market value \( = \text{Rs. } 5.00 - \text{Rs. } 2.25 = \text{Rs. } 2.75 \)
Since the market value (Rs. 2.25) is less than the face value (Rs. 5), the shares were quoted at a discount.
The shares were quoted at a discount of Rs. 2.75.
In simple words: First, find the market price of one share by dividing the total amount paid by the number of shares. Then, compare this market price with the face value of the share. If the market price is lower, it's a discount; if it's higher, it's a premium.

🎯 Exam Tip: Clearly state whether the shares are at a premium or discount by comparing the market value with the face value, and calculate the exact difference.

Question 3. A man sold 600 (Re. 1) shares for Rs. 750. At what price did the shares stand? At what premium or discount were they quoted?
Answer:
Number of shares = 600
Face value of each share = Re. 1
Total market value of 600 shares = Rs. 750
Market value of each share \( = \text{Rs. } \frac {750}{600} = \text{Rs. } \frac {5}{4} = \text{Rs. } 1.25 \)
Difference between market value and face value \( = \text{Rs. } 1.25 - \text{Rs. } 1.00 = \text{Rs. } 0.25 \)
Since the market value (Rs. 1.25) is more than the face value (Re. 1), the shares were quoted at a premium.
The shares were quoted at a premium of Rs. 0.25.
In simple words: Calculate the price per share by dividing the total sale amount by the number of shares. Then, compare this price with the share's face value. If the market price is more, it's a premium; if less, it's a discount.

🎯 Exam Tip: Always specify the exact premium or discount amount, and correctly identify whether it's a premium or a discount based on the market price relative to the face value.

Question 4. A man buys 200 ten rupee shares at Rs. 12.50 each and receives a dividend of 8%. Find the amount invested by him and dividend received.
Answer:
Number of shares bought = 200
Face value of each share = Rs. 10
Market value of each share = Rs. 12.50
Rate of dividend = 8%
Total amount of investment \( = \text{Rs. } 12.50 \times 200 = \text{Rs. } 2500 \)
Total face value of 200 shares \( = \text{Rs. } 10 \times 200 = \text{Rs. } 2000 \)
Dividend received \( = \text{Rs. } 2000 \times \frac {8}{100} = \text{Rs. } 160 \)
In simple words: To find the total money invested, multiply the number of shares by their market value. To find the dividend, multiply the total face value of the shares by the dividend rate. Shares provide a way to invest and earn money.

🎯 Exam Tip: Pay close attention to whether the question asks for investment (uses market value) or dividend calculation (uses face value).

Question 5. A man bought 500 shares, each of face value Rs. 10 of a certain business concern and during the first year after purchase received Rs. 400 as dividend on his shares. Find the rate of dividend on his shares.
Answer:
Number of shares bought = 500
Nominal (face) value of each share = Rs. 10
Amount of dividend received = Rs. 400
Total nominal value of 500 shares \( = \text{Rs. } 10 \times 500 = \text{Rs. } 5000 \)
The dividend on Rs. 5000 is Rs. 400.
Rate of dividend on Rs. 100 \( = \frac{400 \times 100}{5000} = 8\% \)
In simple words: To find the rate of dividend, first work out the total face value of all shares. Then, divide the total dividend received by this total face value and multiply by 100 to get the percentage.

🎯 Exam Tip: The rate of dividend is always a percentage of the total nominal (face) value of the shares, not the investment amount.

Question 6. By purchasing 25 shares for Rs. 40 each a man gets 4 per cent profit on his investment. What rate per cent is the company paying? What is his dividend if he buys 60 shares ?
Answer:
Face value of each share = Rs. 25
Market value of each share = Rs. 40
Percentage profit on investment = 4%
Profit on Rs. 25 face value \( = \text{Rs. } 4 \)
Profit on Rs. 40 market value \( = \frac{4 \times 40}{25} = \frac{160}{25} = \frac{32}{5} = 6.4 \)
So, the rate of dividend the company is paying is 6.4%.
If he buys 60 shares:
Face value of 60 shares \( = \text{Rs. } 25 \times 60 = \text{Rs. } 1500 \)
Dividend on 60 shares \( = \text{Rs. } 1500 \times \frac { 6.4 }{ 100 } = \text{Rs. } 96.0 = \text{Rs. } 96 \)
In simple words: The percentage profit tells you how much the investment grew. To find the company's dividend rate, use the profit percentage on the actual market price. Then, if he buys more shares, calculate the dividend based on the new total face value.

🎯 Exam Tip: Distinguish between "profit on investment" (calculated on market value) and "rate of dividend" (calculated on face value) when solving such problems.

Question 7. Mukul invests Rs. 9000 in a company paying a dividend of 6% per annum when a share of face value 100 stands at Rs. 150. What his annual income? He sells 50% of his shares when the price rises to Rs. 200. What is his gain on this transaction?
Answer:
Investment of Mukul = Rs. 9000
Rate of dividend = 6% p.a.
Face value of each share = Rs. 100
Market value = Rs. 150
Number of shares \( = \text{Rs. } \frac { 9000 }{ 150 } = 60 \)
Face value of 60 shares \( = \text{Rs. } 100 \times 60 = \text{Rs. } 6000 \)
Amount of annual dividend (income) \( = \text{Rs. } \frac{6000 \times 6}{100} = \text{Rs. } 360 \)
When the price rises to Rs. 200, he sells 50% of his shares.
Number of shares sold \( = 60 \times \frac { 50 }{ 100 } = 30 \)
Market value of each share when sold = Rs. 200
Amount received from selling 30 shares \( = \text{Rs. } 200 \times 30 = \text{Rs. } 6000 \)
Market value of remaining 30 shares \( = \text{Rs. } 150 \times 30 = \text{Rs. } 4500 \) (This is Mukul's initial investment value for the remaining shares, though not directly used in calculating gain from the *sold* shares transaction itself, but implicitly for total profit/loss)
Total amount received (from sale) = Rs. 6000
Initial cost of 30 shares \( = 30 \times \text{Rs. } 150 = \text{Rs. } 4500 \)
Gain on this transaction (sale) \( = \text{Rs. } 6000 - \text{Rs. } 4500 = \text{Rs. } 1500 \)
In simple words: First, calculate the total number of shares bought and his annual earnings from dividends. When he sells some shares, find out how much money he gets from the sale and compare it to what he originally paid for those specific shares to see his profit.

🎯 Exam Tip: Be careful to calculate the profit only on the shares that are sold. The annual income is based on the total shares held before any sale.

Question 8. By investing Rs. 7500 in a company paying 10% dividend, an income of Rs. 500 is received. What price is paid for each Rs. 100 share?
Answer:
Investment = Rs. 7500
Rate of dividend = 10%
Total income (dividend) = Rs. 500
Face value of each share = Rs. 100
Total face value of shares \( = \text{Rs. } \frac{500 \times 100}{10} = \text{Rs. } 5000 \)
Number of shares \( = \text{Rs. } \frac{5000}{100} = 50 \)
Now, the market value of 50 shares is Rs. 7500 (total investment).
Market value of each share \( = \text{Rs. } \frac { 7500 }{ 50 } = \text{Rs. } 150 \)
In simple words: We know the total investment, dividend rate, and the income received. We need to find the price of one share. First, use the income and dividend rate to find the total face value of shares. Then, find the number of shares. Finally, divide the total investment by the number of shares to get the market price of one share.

🎯 Exam Tip: When working backwards to find the market value, use the total investment and the number of shares. The dividend helps you find the total face value first.

Question 9. Arun owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate:
(i) the dividend Arun would receive, and
(ii) the rate of interest, on his investment. Considering that Arun bought these shares @ Rs. 30 per share in the market.
Answer:
Number of shares Arun has = 560
Face value of each share = Rs. 25
Rate of dividend = 9%
Market price paid for each share = Rs. 30
Total face value of 560 shares \( = \text{Rs. } 25 \times 560 = \text{Rs. } 14000 \)
(i) Total dividend received by Arun \( = \text{Rs. } 14000 \times 9\% \)
\( = \text{Rs. } 14000 \times \frac { 9 }{ 100 } = \text{Rs. } 1260 \)
(ii) Total investment \( = \text{Rs. } 30 \times 560 = \text{Rs. } 16800 \)
Rate of interest (return) on his investment \( = \frac{\text{Dividend}}{\text{Investment}} \times 100\% \)
\( = \frac{1260 \times 100}{16800} \% = 7.5 \% \)
In simple words: First, calculate the total face value of all shares to find the dividend amount. Then, figure out the total money Arun spent (his investment) and use this along with the dividend to calculate the percentage return on his money.

🎯 Exam Tip: Remember to calculate dividend based on face value and rate of interest/return based on the actual investment (market value). Also, ensure correct use of the given market price in calculating investment.

Question 10. What sum should Ashok invest in 25 shares selling at Rs. 36 to obtain an income of Rs. 720, if the dividend declared is 12%. Also find :
(i) the number of shares bought by Ashok.
(ii) the percentage return on his investment.
Answer:
Face value of each share = Rs. 25
Market value of each share = Rs. 36
Total income (dividend) = Rs. 720
Rate of dividend = 12%
(i) Total face value of shares \( = \frac{\text{Total Income} \times 100}{\text{Rate of dividend}} = \frac{720 \times 100}{12} = \text{Rs. } 6000 \)
Number of shares bought by Ashok \( = \frac{\text{Total face value}}{\text{Face value of each share}} = \frac { 6000 }{ 25 } = 240 \)
Sum Ashok should invest \( = \text{Number of shares} \times \text{Market value of each share} \)
\( = 240 \times \text{Rs. } 36 = \text{Rs. } 8640 \)
(ii) Percentage return on his investment \( = \frac{\text{Total Income}}{\text{Total Investment}} \times 100\% \)
\( = \frac{720 \times 100}{8640} \% = \frac{72000}{8640} \% \)
\( = \frac { 25 }{ 3 } \% = 8\frac { 1 }{ 3 }% \approx 8.33\% \)
In simple words: To find how much Ashok should invest, first calculate the total face value of shares needed to get his desired income. Then, find the number of shares. Finally, multiply the number of shares by their market price to get the investment amount. The percentage return is his total income divided by his investment, multiplied by 100.

🎯 Exam Tip: Ensure that the total investment is calculated using the market value of shares, and the number of shares is derived from the income and face value.

Question 11. Mr. Sharma has 60 shares of nominal value 7100 and he 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, paying 18% dividend annually. Calculate:
(i) the sale proceeds.
(ii) the number of shares he buys.
(iii) the annual dividend from these shares.
Answer:
**Part 1: Selling the old shares**
Number of shares = 60
Face value of each share = Rs. 100 (assuming 7100 is a typo and should be 100 as per general share value conventions, since 7100 nominal value for 60 shares is unusual, and 100 is typical for such problems. If 7100 is intended as total nominal value, then it would be different, but face value per share makes more sense for "nominal value")
Market value = 60% premium on face value
\( = \text{Rs. } 100 + (60\% \text{ of } 100) = \text{Rs. } 100 + 60 = \text{Rs. } 160 \)
(i) Sale proceeds \( = \text{Number of shares} \times \text{Market value of each share} \)
\( = 60 \times \text{Rs. } 160 = \text{Rs. } 9600 \)

**Part 2: Investing the proceeds in new shares**
Nominal value of new share purchased = Rs. 50
Market value of new share = 4% discount on nominal value
\( = \text{Rs. } 50 - (\frac { 50 \times 4 }{ 100 }) = \text{Rs. } 50 - 2 = \text{Rs. } 48 \)
(ii) Number of shares purchased \( = \frac{\text{Sale proceeds}}{\text{Market value of new share}} = \frac { 9600 }{ 48 } = 200 \)

**Part 3: Annual dividend from new shares**
Rate of dividend = 18% p.a.
Face value of 200 new shares \( = \text{Rs. } 50 \times 200 = \text{Rs. } 10000 \)
(iii) Annual dividend \( = \text{Rs. } 10000 \times \frac { 18 }{ 100 } = \text{Rs. } 1800 \)
In simple words: First, calculate the total money Mr. Sharma gets from selling his old shares, including any premium. Then, use this money to buy new shares, taking into account their discounted market price. Finally, calculate the yearly dividend he will receive from these new shares based on their total face value.

🎯 Exam Tip: Clearly separate the calculations for selling old shares and buying new ones. Remember that premium/discount applies to market value, but dividend is always on face value.

Question 12. A man invests a sum of money in Rs. 100 shares, paying 15% dividend, quoted at 20% premium. If his annual dividend is Rs. 540, calculate:
(i) his total investment.
(ii) the rate of return on his investment.
Answer:
Face value of each share = Rs. 100
Rate of dividend = 15%
Shares quoted at 20% premium.
Annual dividend (income) = Rs. 540
Market value of each share \( = \text{Rs. } 100 + (20\% \text{ of } 100) = \text{Rs. } 100 + 20 = \text{Rs. } 120 \)
(i) Total face value of shares \( = \frac{\text{Annual Dividend} \times 100}{\text{Rate of Dividend}} = \frac{540 \times 100}{15} = \text{Rs. } 3600 \)
Number of shares \( = \frac{\text{Total Face Value}}{\text{Face value of each share}} = \frac{3600}{100} = 36 \)
His total investment \( = \text{Number of shares} \times \text{Market value of each share} \)
\( = 36 \times \text{Rs. } 120 = \text{Rs. } 4320 \)
(ii) Rate of return on his investment \( = \frac{\text{Annual Dividend}}{\text{Total Investment}} \times 100\% \)
\( = \frac{540 \times 100}{4320} \% = \frac{54000}{4320} \% \)
\( = \frac { 100 }{ 8 }% = 12.5\% \)
In simple words: First, use the annual dividend and dividend rate to find the total face value of shares. Then, calculate the number of shares and multiply by their market value (including premium) to get the total investment. Finally, divide the dividend by the investment to find the percentage return.

🎯 Exam Tip: Be careful with the market value calculation involving premium, and ensure the dividend is correctly related to the face value of shares to find the total face value first.

Question 13. A lady holds 1800 hundred rupee shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return would she have got on her investment? Give your answer to the nearest integer.
Answer:
Number of shares = 1800
Face value of each share = Rs. 100
Dividend rate = 15%
Total face value of shares \( = 1800 \times \text{Rs. } 100 = \text{Rs. } 180000 \)
Annual dividend \( = \text{Rs. } 180000 \times 15\% \)
\( = \text{Rs. } 180000 \times \frac{15}{100} = \text{Rs. } 27000 \)

If she had bought these shares at 40% premium:
Market value of each share \( = \text{Rs. } 100 + (40\% \text{ of } 100) = \text{Rs. } 100 + 40 = \text{Rs. } 140 \)
(ii) Total investment \( = \text{Number of shares} \times \text{Market value of each share} \)
\( = 1800 \times \text{Rs. } 140 = \text{Rs. } 252000 \)
Percentage return on investment \( = \frac{\text{Annual Dividend}}{\text{Total Investment}} \times 100\% \)
\( = \frac{27000 \times 100}{252000} \% \)
\( = \frac{2700000}{252000} \% = \frac { 2700 }{ 252 } \% = \frac { 675 }{ 63 } \% = \frac { 75 }{7} \% \approx 10.71 \% \)
Rounding to the nearest integer, the percentage return is 11%.
In simple words: First, calculate the total annual dividend based on the shares' face value. If she bought them at a premium, calculate her total investment. Then, divide the dividend by her investment and multiply by 100 to find the percentage return, rounding the final answer to a whole number.

🎯 Exam Tip: Be sure to calculate the annual dividend first, and then use the *actual* investment amount (which includes any premium paid) to determine the percentage return. Remember to round to the nearest integer as requested.

Question 14. A man invests Rs. 11200 in a company paying 6% dividend when its Rs. 100 share can be bought for 140. Find:
(i) his annual income.
(ii) the percentage income on his investment.
Answer:
Investment = Rs. 11200
Rate of dividend = 6%
Face value of each share = Rs. 100
Market value of each share = Rs. 140
Number of shares bought \( = \frac{\text{Investment}}{\text{Market value of each share}} = \frac { 11200 }{ 140 } = 80 \)
Total face value of shares \( = 80 \times \text{Rs. } 100 = \text{Rs. } 8000 \)
(i) Annual income (dividend) \( = \text{Rs. } 8000 \times 6\% \)
\( = \text{Rs. } 8000 \times \frac{6}{100} = \text{Rs. } 480 \)
(ii) Percentage income on his investment \( = \frac{\text{Annual Income}}{\text{Investment}} \times 100\% \)
\( = \frac{480 \times 100}{11200} \% = \frac{48000}{11200} \% \)
\( = \frac{480}{112} \% = \frac{30}{7} \% = 4\frac { 2 }{ 7 }% \)
In simple words: First, find out how many shares the man bought by dividing his total investment by the market price per share. Then, calculate his annual income using the total face value of these shares and the dividend rate. Finally, calculate the percentage income by dividing his annual income by his total investment and multiplying by 100.

🎯 Exam Tip: Remember to calculate the number of shares first. Income (dividend) is always based on the face value, while percentage income (return) is based on the actual investment.

Question 15. 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 would 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 had paid for each share.
Answer:
Number of shares in the company = 10000
Face value of each share = Rs. 100
Rate of annual dividend = 5%
(i) Total amount of dividend paid by the company \( = \text{Total number of shares} \times \text{Face value of each share} \times \text{Rate of dividend} \)
\( = 10000 \times \text{Rs. } 100 \times 5\% \)
\( = \text{Rs. } 1000000 \times \frac{5}{100} = \text{Rs. } 50,000 \)
(ii) Annual income on 72 shares for a man:
Face value of 72 shares \( = 72 \times \text{Rs. } 100 = \text{Rs. } 7200 \)
Income on 72 shares \( = \text{Rs. } 7200 \times 5\% \)
\( = \text{Rs. } 7200 \times \frac{5}{100} = \text{Rs. } 360 \)
(iii) If he received only 4% on his investment:
Let the market value of each share be \( x \).
Investment for 72 shares \( = 72 \times x = \text{Rs. } 72x \)
Rate of return on investment = 4%
We know, Annual Income \( = \text{Investment} \times \text{Rate of Return} \)
Rs. 360 \( = \text{Rs. } 72x \times 4\% \)
Rs. 360 \( = 72x \times \frac{4}{100} \)
\( 360 = \frac{288x}{100} \)
\( x = \frac{360 \times 100}{288} = \frac{36000}{288} = \text{Rs. } 125 \)
The price he had paid for each share (market value) was Rs. 125.
In simple words: First, calculate the total dividend the company pays based on all its shares. Then, find the income for an individual holding a certain number of shares. Finally, if the person knows their percentage return, you can work backward to find the price they paid for each share.

🎯 Exam Tip: Carefully distinguish between the total dividend paid by the company (based on total shares) and an individual's income. When finding market value from return, equate the income to a percentage of the investment.

Question 16. A man invests Rs. 1680 in buying shares of nominal value 24 and selling at 12% premium. The dividend on the shares is 15% per annum.
(i) Calculate the number of shares he buys.
(ii) Calculate the dividend he receives annually. (ICSE 1999)
Answer:
Investment = Rs. 1680
Nominal value of each share = Rs. 24
Shares selling at 12% premium.
Market value of each share \( = \text{Rs. } 24 + (12\% \text{ of } 24) = \text{Rs. } 24 + \frac{24 \times 12}{100} \)
\( = \text{Rs. } 24 + \frac{288}{100} = \text{Rs. } 24 + 2.88 = \text{Rs. } 26.88 \)
(i) Number of shares he buys \( = \frac{\text{Investment}}{\text{Market value of each share}} = \frac { 1680 }{ 26.88 } \)
\( = \frac{1680 \times 100}{2688} = \frac { 168000 }{ 2688 } = 62.5 \) shares
(ii) Rate of dividend = 15% p.a.
Total nominal value of shares \( = 62.5 \times \text{Rs. } 24 = \text{Rs. } 1500 \)
Dividend he receives annually \( = \text{Rs. } 1500 \times 15\% \)
\( = \text{Rs. } 1500 \times \frac{15}{100} = \text{Rs. } 225 \)
In simple words: First, calculate the market value of each share by adding the premium to the nominal value. Then, divide the total investment by this market value to find the number of shares. Finally, calculate the annual dividend based on the total nominal value of these shares and the dividend rate.

🎯 Exam Tip: Be careful with decimal calculations for market value and number of shares. The dividend is always calculated on the nominal value, not the market value or investment.

Question 17. A man invests Rs. 7425 on buying share of face value Rs. 90 each at a premium of 10% in a company. If he earns Rs. 1350 as dividend at the end of the year, find
(i) the number of shares he has in the company.
(ii) the dividend percentage per share that he received.
Answer:
Investment = Rs. 7425
Face value of each share = Rs. 90
Shares are bought at a premium of 10%.
Market value of each share \( = \text{Rs. } 90 + (10\% \text{ of } 90) = \text{Rs. } 90 + 9 = \text{Rs. } 99 \)
Amount of dividend received = Rs. 1350
(i) Number of shares he has in the company \( = \frac{\text{Investment}}{\text{Market value of each share}} = \frac { 7425 }{ 99 } = 75 \)
Total face value of 75 shares \( = 75 \times \text{Rs. } 90 = \text{Rs. } 6750 \)
(ii) Dividend percentage per share (Rate of dividend) \( = \frac{\text{Total Dividend}}{\text{Total Face Value}} \times 100\% \)
\( = \frac{1350 \times 100}{6750} \% = \frac{135000}{6750} \% = 20\% \)
In simple words: First, calculate the market value of each share by adding the premium to its face value. Then, divide the total investment by this market value to find the number of shares. Finally, use the total dividend received and the total face value of the shares to calculate the dividend percentage.

🎯 Exam Tip: Always calculate the market value first when shares are bought at a premium. The dividend percentage is always a ratio of total dividend to total face value.

Question 18. Abhishek sold a certain number of shares of Rs. 20 paying 8% dividend at Rs. 18 and invested the proceeds in 10 shares, paying 12% dividend at 50% premium. If the change in his annual income is Rs. 120, find the number of shares sold by him ?
Answer:
Let the number of shares sold by Abhishek be \( x \).

**First case (Old shares):**
Face value of each share = Rs. 20
Rate of dividend = 8%
Market value of each share = Rs. 18
Sale proceeds by selling \( x \) shares \( = \text{Rs. } 18 \times x = \text{Rs. } 18x \)
Total face value of \( x \) shares \( = \text{Rs. } 20 \times x = \text{Rs. } 20x \)
Dividend from old shares \( = \text{Rs. } 20x \times 8\% = \text{Rs. } 20x \times \frac{8}{100} = \text{Rs. } \frac { 160x }{ 100 } = \text{Rs. } \frac { 8x }{ 5 } \)

**Second case (New shares):**
Abhishek invests the proceeds (Rs. \( 18x \)) into new shares.
Face value of new each share = Rs. 10
Market value of new shares = 50% premium
\( = \text{Rs. } 10 + (50\% \text{ of } 10) = \text{Rs. } 10 + 5 = \text{Rs. } 15 \)
Number of new shares purchased \( = \frac{\text{Investment}}{\text{Market value of new share}} = \frac { 18x }{ 15 } = \frac { 6x }{ 5 } \)
Total face value of new shares \( = \frac { 6x }{ 5 } \times \text{Rs. } 10 = \text{Rs. } 12x \)
Rate of dividend for new shares = 12%
Dividend from new shares \( = \text{Rs. } 12x \times 12\% = \text{Rs. } 12x \times \frac{12}{100} = \text{Rs. } \frac { 144x }{ 100 } = \text{Rs. } \frac { 36x }{ 25 } \)

**Change in annual income:**
Difference in dividend \( = \text{Dividend from new shares} - \text{Dividend from old shares} \)
\( = \text{Rs. } \frac { 36x }{ 25 } - \text{Rs. } \frac { 8x }{ 5 } \)
\( = \text{Rs. } \frac { 36x - (8x \times 5) }{ 25 } = \text{Rs. } \frac { 36x - 40x }{ 25 } = \text{Rs. } \frac { -4x }{ 25 } \)
The problem states a change in income of Rs. 120. A negative value means a decrease in income. We take the absolute change.
\( \frac { 4x }{ 25 } = 120 \)
\( 4x = 120 \times 25 \)
\( 4x = 3000 \)
\( x = \frac{3000}{4} = 750 \)
The number of shares sold by him is 750.
In simple words: First, calculate the dividend from the shares Abhishek sold. Then, find out how many new shares he bought with the money and calculate the dividend from those. The difference between the new and old dividends is given as Rs. 120. Set up an equation with this information to find the number of shares he originally sold.

🎯 Exam Tip: This problem involves two stages of investment. Calculate the income from each stage separately and then use the difference in income to find the unknown variable. Pay attention to face value vs. market value in each step.

Question 19. A person invested Rs. 8000 and 10000 in buying shares of two companies which later on declared dividends of 12% and 8% respectively. He collects the dividends and sells out his shares at a loss of 2% and 3% respectively. Find his total earning from the above transaction.
Answer:
**First case (Company 1):**
Investment = Rs. 8000
Rate of dividend = 12%
Income (dividend) \( = \text{Rs. } 8000 \times 12\% = \text{Rs. } 8000 \times \frac{12}{100} = \text{Rs. } 960 \)
Loss on selling shares = 2%
Loss amount \( = \text{Rs. } 8000 \times 2\% = \text{Rs. } 8000 \times \frac{2}{100} = \text{Rs. } 160 \)

**Second case (Company 2):**
Investment = Rs. 10000
Rate of dividend = 8%
Income (dividend) \( = \text{Rs. } 10000 \times 8\% = \text{Rs. } 10000 \times \frac{8}{100} = \text{Rs. } 800 \)
Loss on selling shares = 3%
Loss amount \( = \text{Rs. } 10000 \times 3\% = \text{Rs. } 10000 \times \frac{3}{100} = \text{Rs. } 300 \)

**Total Earning:**
Total income from dividends \( = \text{Rs. } 960 + \text{Rs. } 800 = \text{Rs. } 1760 \)
Total loss from selling shares \( = \text{Rs. } 160 + \text{Rs. } 300 = \text{Rs. } 460 \)
Net gain (total earning) \( = \text{Total income} - \text{Total loss} \)
\( = \text{Rs. } 1760 - \text{Rs. } 460 = \text{Rs. } 1300 \)
In simple words: First, calculate the dividend income and the loss from selling shares for each company separately. Then, add up all the dividend incomes to get the total income. Add up all the losses from selling shares to get the total loss. Finally, subtract the total loss from the total income to find the overall earning.

🎯 Exam Tip: Treat each company's transaction separately for income and loss calculations, then combine them to find the net gain or loss from the entire process.

Question 20. A person invested 20%, 30% and 25% of his savings in buying shares of three different companies A, B and C, which declared dividends of 10%, 12% and 15% respectively. If his total income on account of dividends be Rs. 2337.50, find his saving and the amount which he invested in buying shares of each company.
Answer:
Let the total savings of the person be Rs. \( x \).

**Investment in Company A:**
Investment \( = 20\% \text{ of } x = \frac { 20 }{ 100 } x = \frac { x }{ 5 } \)
Dividend rate = 10%
Income from Company A \( = \frac { x }{ 5 } \times 10\% = \frac { x }{ 5 } \times \frac { 10 }{ 100 } = \frac { 10x }{ 500 } = \frac { x }{ 50 } \)

**Investment in Company B:**
Investment \( = 30\% \text{ of } x = \frac { 30 }{ 100 } x = \frac { 3x }{ 10 } \)
Dividend rate = 12%
Income from Company B \( = \frac { 3x }{ 10 } \times 12\% = \frac { 3x }{ 10 } \times \frac { 12 }{ 100 } = \frac { 36x }{ 1000 } = \frac { 9x }{ 250 } \)

**Investment in Company C:**
Investment \( = 25\% \text{ of } x = \frac { 25 }{ 100 } x = \frac { x }{ 4 } \)
Dividend rate = 15%
Income from Company C \( = \frac { x }{ 4 } \times 15\% = \frac { x }{ 4 } \times \frac { 15 }{ 100 } = \frac { 15x }{ 400 } = \frac { 3x }{ 80 } \)

**Total Income:**
Total income from dividends \( = \frac { x }{ 50 } + \frac { 9x }{ 250 } + \frac { 3x }{ 80 } \)
To add these, find a common denominator, which is 2000.
\( = \frac { (x \times 40) + (9x \times 8) + (3x \times 25) }{ 2000 } = \frac { 40x + 72x + 75x }{ 2000 } = \frac { 187x }{ 2000 } \)
Given total income = Rs. 2337.50
So, \( \frac { 187x }{ 2000 } = 2337.50 \)
\( 187x = 2337.50 \times 2000 \)
\( 187x = 4675000 \)
\( x = \frac{4675000}{187} = 25000 \)
The total savings of the person is Rs. 25000.

**Amount invested in each company:**
Investment in A Company \( = \frac { x }{ 5 } = \frac { 25000 }{ 5 } = \text{Rs. } 5000 \)
Investment in B Company \( = \frac { 3x }{ 10 } = \frac { 3 \times 25000 }{ 10 } = \text{Rs. } 7500 \)
Investment in C Company \( = \frac { x }{ 4 } = \frac { 25000 }{ 4 } = \text{Rs. } 6250 \)
In simple words: First, represent the total savings as 'x'. Then, calculate the investment amount for each company as a percentage of 'x', and find the dividend income from each. Add up all the dividend incomes and set it equal to the given total income to find 'x'. Once 'x' is known, calculate the actual investment amount for each company.

🎯 Exam Tip: This problem requires setting up an algebraic equation based on the total income. Be careful with percentage calculations and finding the common denominator when adding fractions of 'x'.

Question 1. A dividend of 9% was declared on Rs. 100 shares selling at a certain price. If the rate of return is \( 7\frac { 1 }{ 2 }% \), calculate :
(i) the market value of the share
(ii) the amount to be invested to obtain an annual dividend of Rs. 630.
Answer:
Face value of each share = Rs. 100
Rate of dividend = 9%
Rate of return on investment \( = 7\frac { 1 }{ 2 }% = \frac { 15 }{ 2 }% \)
Let the market price of each share be Rs. \( x \).
Dividend per share \( = 9\% \text{ of Rs. } 100 = \text{Rs. } 9 \)
(i) We know, Rate of return \( = \frac{\text{Dividend per share}}{\text{Market value per share}} \times 100\% \)
\( \frac { 15 }{ 2 }% = \frac { 9 }{ x } \times 100\% \)
\( \frac { 15 }{ 2 } = \frac { 900 }{ x } \)
\( 15x = 900 \times 2 \)
\( 15x = 1800 \)
\( x = \frac{1800}{15} = \text{Rs. } 120 \)
The market value of each share is Rs. 120.

(ii) To obtain an annual dividend of Rs. 630.
Total face value required \( = \frac{\text{Desired Dividend}}{\text{Rate of Dividend}} \times 100 = \frac{630}{9} \times 100 = \text{Rs. } 7000 \)
Number of shares required \( = \frac{\text{Total Face Value}}{\text{Face value of each share}} = \frac{7000}{100} = 70 \)
Amount to be invested \( = \text{Number of shares} \times \text{Market value of each share} \)
\( = 70 \times \text{Rs. } 120 = \text{Rs. } 8400 \)
In simple words: To find the market value, use the dividend per share and the rate of return. To find the investment needed for a specific dividend, first calculate the total face value required, then the number of shares, and finally multiply by the market value per share.

🎯 Exam Tip: Clearly use the dividend per share (calculated on face value) and the rate of return (on market value) to find the unknown market value. Remember that total investment uses market value, but total dividend calculation uses face value.

Question 2. A man invests Rs. 8800 in buying shares of face value of rupees hundred each at a premium of 10% in a company. If he earns Rs. 1200 at the end of the year as dividend, find
(i) the number of shares he has in the company ?
(ii) the dividend percentage per share.
Answer:
Investment = Rs. 8800
Face value of each share = Rs. 100
Market value at a premium of 10% \( = \text{Rs. } 100 + (10\% \text{ of } 100) = \text{Rs. } 100 + 10 = \text{Rs. } 110 \)
Total dividend received = Rs. 1200
(i) Number of shares he has in the company \( = \frac{\text{Investment}}{\text{Market value per share}} = \frac { 8800 }{ 110 } = 80 \)
(ii) To find the dividend percentage per share (rate of dividend):
Total face value of 80 shares \( = 80 \times \text{Rs. } 100 = \text{Rs. } 8000 \)
Rate of dividend per share \( = \frac{\text{Total Dividend}}{\text{Total Face Value}} \times 100\% \)
\( = \frac{1200}{8000} \times 100\% = \frac{120000}{8000} \% = 15\% \)
In simple words: First, calculate the market value of each share by adding the premium to the face value. Then, divide the total investment by this market value to find how many shares the man bought. Finally, use the total dividend he received and the total face value of his shares to calculate the dividend percentage.

🎯 Exam Tip: Be careful to use the market value for calculating the number of shares from investment, and use the face value for calculating the dividend percentage from the total dividend received.

Question 3. A man wants to buy 62 shares available at Rs. 132 (par value of Rs. 100).
(i) How much should he invest ?
(ii) If the dividend is 7.5%, what will be his annual income?
(iii) If he wants to increase income by Rs. 150, how many extra shares should he buy?
Answer:
Number of shares = 62
Market value of each share = Rs. 132
Face value of each share = Rs. 100
(i) His investment \( = \text{Number of shares} \times \text{Market value of each share} \)
\( = 62 \times \text{Rs. } 132 = \text{Rs. } 8184 \)
(ii) Rate of dividend = 7.5% p.a. \( = \frac { 15 }{ 2 }% \)
Total face value of 62 shares \( = 62 \times \text{Rs. } 100 = \text{Rs. } 6200 \)
Annual income (dividend) \( = \text{Rs. } 6200 \times 7.5\% \)
\( = \text{Rs. } 6200 \times \frac { 15 }{ 2 \times 100 } = \text{Rs. } 62 \times \frac { 15 }{ 2 } = \text{Rs. } 31 \times 15 = \text{Rs. } 465 \)
(iii) Extra income he wants = Rs. 150
New desired annual income \( = \text{Rs. } 465 + \text{Rs. } 150 = \text{Rs. } 615 \)
Let the new total number of shares be \( N \).
New total income \( = N \times \text{Face value of each share} \times \text{Rate of dividend} \)
\( 615 = N \times \text{Rs. } 100 \times 7.5\% \)
\( 615 = N \times \text{Rs. } 100 \times \frac { 15 }{ 2 \times 100 } \)
\( 615 = N \times \frac { 15 }{ 2 } \)
\( N = \frac{615 \times 2}{15} = \frac{1230}{15} = 82 \)
New number of shares needed = 82
Extra shares he has to buy \( = \text{New total shares} - \text{Current shares} \)
\( = 82 - 62 = 20 \)
He should buy 20 extra shares.
In simple words: First, calculate the total money he needs to invest for 62 shares. Then, find his annual income from these shares using the dividend rate. If he wants to earn more money, calculate the total number of shares he would need for that higher income, and subtract his current shares to find how many more he needs to buy.

🎯 Exam Tip: Remember that investment is based on market value, while annual income (dividend) is based on face value. For increasing income, calculate the *total* shares required for the new income, then find the difference.

Question 4. A man invests Rs. 20,020 in buying shares of nominal value 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:
Investment = Rs. 20020
Nominal value of each share = Rs. 26
Shares are at 10% premium.
Market value of each share \( = \text{Rs. } 26 + (10\% \text{ of } 26) = \text{Rs. } 26 + \frac{26 \times 10}{100} \)
\( = \text{Rs. } 26 + \frac{260}{100} = \text{Rs. } 26 + 2.60 = \text{Rs. } 28.60 \)
Rate of dividend = 15%
(i) Number of shares he buys \( = \frac{\text{Investment}}{\text{Market value of each share}} = \frac { 20020 }{ 28.60 } \)
\( = \frac{20020 \times 100}{2860} = \frac{2002000}{2860} = 700 \)
He buys 700 shares.

(ii) Total nominal value of 700 shares \( = 700 \times \text{Rs. } 26 = \text{Rs. } 18200 \)
Dividend he receives annually \( = \text{Rs. } 18200 \times 15\% \)
\( = \text{Rs. } 18200 \times \frac{15}{100} = \text{Rs. } 2730 \)

(iii) Rate of interest (return) on his investment \( = \frac{\text{Dividend received}}{\text{Investment}} \times 100\% \)
\( = \frac{2730 \times 100}{20020} \% = \frac{273000}{20020} \% \approx 13.636 \% \)
Rounded to two decimal places, the rate of interest is 13.64%.
In simple words: First, calculate the market value of each share, including the premium. Then, divide the total investment by this market value to find the number of shares bought. Next, calculate the annual dividend based on the total nominal value of these shares. Finally, find the percentage return by dividing the annual dividend by the total investment and multiplying by 100.

🎯 Exam Tip: Be careful with decimal calculations for market value. Always remember that the number of shares is found from investment and market value, while dividend calculation uses nominal (face) value.

Question 5. A man invested Rs. 45,000 in 15% Rs. 100 shares quoted at 125. When the market value of these shares rose to Rs. 140, he sold some shares, just enough to raise Rs. 8400. Calculate :
(i) the number of shares he still holds;
(ii) the dividend due to him on these remaining shares.
Answer:
Total Investment = Rs. 45000
Face Value of each share = Rs. 100
Market Value of each share (at purchase) = Rs. 125
Rate of Dividend = 15%
Number of shares bought = \( \frac{45000}{125} = 360 \) shares.
He sold some shares when the price was Rs. 140 each.
(i) Amount raised by selling shares = Rs. 8400
Number of shares sold = \( \frac{8400}{140} = 60 \) shares.
Remaining shares = \( 360 - 60 = 300 \) shares.
(ii) Dividend on remaining shares = \( 300 \times \text{Face Value per share} \times \text{Rate of Dividend} \)
= \( 300 \times 100 \times \frac{15}{100} = Rs. 4500 \)
In simple words: First, we found out how many shares the man bought. Then we calculated how many shares he sold to get a certain amount of money. The remaining shares are what he still owns, and the dividend is the income from these shares. This shows how selling some shares impacts future earnings.

🎯 Exam Tip: Remember that dividends are always calculated on the face value (nominal value) of the shares, not on the market value or investment amount.

Question 6. Mr. Tewari invested Rs. 29,040 in 15%, Rs. 100 shares quoted at a premium of 20%. Calculate :
(i) The number of shares bought by Mr. Tewari.
(ii) Mr. Tewari's income from the investment.
(iii) The percentage return on his investment.
Answer:
Investment made by Mr. Tewari = Rs. 29040
Face value of each share = Rs. 100
The shares are quoted at a premium of 20%.
Market value of each share = \( \text{Rs. } 100 + (20\% \text{ of Rs. } 100) = \text{Rs. } 100 + 20 = \text{Rs. } 120 \)
Rate of dividend = 15%
(i) Number of shares bought by Mr. Tewari = \( \frac{\text{Investment}}{\text{Market Value per share}} = \frac{29040}{120} = 242 \) shares.
(ii) Mr. Tewari's income from the investment (annual dividend) = \( \text{Number of shares} \times \text{Face Value per share} \times \text{Rate of Dividend} \)
= \( 242 \times 100 \times \frac{15}{100} = Rs. 3630 \)
(iii) The percentage return on his investment = \( \frac{\text{Annual Income}}{\text{Total Investment}} \times 100 \)
= \( \frac{3630}{29040} \times 100 = 12.5\% \)
In simple words: First, we found the actual price per share by adding the premium to the face value. Then we calculated how many shares were bought with the total investment. The income is the dividend from these shares, and the percentage return shows how much profit was made compared to the money invested.

🎯 Exam Tip: Always distinguish between face value (used for calculating dividend) and market value (used for calculating investment and number of shares bought/sold).

Question 7. Mr. Ram Gopal invested Rs. 8000 in 7% Rs. 100 shares at Rs. 80. After a year he sold these shares at 75 each and invested the proceeds (including his dividend) in 18%, Rs. 25 shares at 41. Find :
(i) his dividend for the first year.
(ii) his annual income in the second year.
(iii) the percentage increase in his return on his original investment.
Answer:
Initial investment made by Ram Gopal = Rs. 8000
Face value of each share = Rs. 100
Market value of each share (initial purchase) = Rs. 80
Rate of dividend (first year) = 7%
Number of shares bought = \( \frac{\text{Investment}}{\text{Market Value per share}} = \frac{8000}{80} = 100 \) shares.
(i) Dividend for the first year = \( \text{Number of shares} \times \text{Face Value per share} \times \text{Rate of Dividend} \)
= \( 100 \times 100 \times \frac{7}{100} = Rs. 700 \)
After a year, he sold these shares at Rs. 75 each.
Sale proceeds = \( 100 \times 75 = Rs. 7500 \)
Total amount available for second investment (proceeds + first year dividend) = \( \text{Rs. } 7500 + \text{Rs. } 700 = \text{Rs. } 8200 \)
New shares: Face value = Rs. 25, Market value = Rs. 41, Rate of dividend = 18%
Number of shares bought in second investment = \( \frac{8200}{41} = 200 \) shares.
Nominal value of 200 shares = \( 200 \times 25 = Rs. 5000 \)
(ii) Annual income in the second year (dividend) = \( \text{Nominal Value of shares} \times \text{Rate of Dividend} \)
= \( 5000 \times \frac{18}{100} = Rs. 900 \)
(iii) Increase in income = \( \text{Second year income} - \text{First year income} = \text{Rs. } 900 - \text{Rs. } 700 = \text{Rs. } 200 \)
Percentage increase in return on original investment = \( \frac{\text{Increase in income}}{\text{Original Investment}} \times 100 \)
= \( \frac{200}{8000} \times 100 = 2.5\% \)
In simple words: This problem tracks an investment over two years. First, we find the income from the initial shares. Then, the shares are sold, and the money, plus the first year's income, is reinvested. We calculate the new income from this second investment and then find how much the income grew compared to the start. This shows how re-investing profits can change returns.

🎯 Exam Tip: When calculating percentage increase, make sure to use the correct base value (in this case, the original investment of Rs. 8000) for the comparison.

Question 8. Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate :
(i) The dividend that Ajay will get.
(ii) The rate of interest on his investment, if Ajay had paid Rs. 30 for each share.
Answer:
Number of shares Ajay owns = 560
Face value of each share = Rs. 25
Rate of dividend = 9%
(i) To calculate the dividend Ajay will get, first find the total face value of his shares:
Total face value of 560 shares = \( 560 \times 25 = Rs. 14000 \)
Dividend received by Ajay = \( \text{Total Face Value} \times \text{Rate of Dividend} \)
= \( 14000 \times \frac{9}{100} = Rs. 1260 \)
(ii) If Ajay paid Rs. 30 for each share, his total investment would be:
Total investment = \( 560 \times 30 = Rs. 16800 \)
Rate of interest on his investment (return) = \( \frac{\text{Dividend Received}}{\text{Total Investment}} \times 100 \)
= \( \frac{1260}{16800} \times 100 = 7.5\% \)
In simple words: We first find the total value of all shares at their original (face) price and then calculate the dividend based on that. Then, knowing what Ajay actually paid for the shares, we figure out what percentage of his own money he got back. The dividend is the profit shared, and the interest rate shows the return on the actual money spent.

🎯 Exam Tip: Always remember that dividend calculations use the face value of the shares, while the rate of interest on investment uses the market value (or actual investment amount).

Question 9. A company with 4000 shares of nominal value of Rs. 110 each declares an annual dividend of 15%. Calculate:
(i) The total amount of dividend paid by the company.
(ii) The annual income of Shah Rukh who holds 88 shares in the company.
(iii) If he received only 10% on his investment, find the price Shah Rukh paid for each share.
Answer:
Total number of shares in the company = 4000
Nominal value (Face value) of each share = Rs. 110
Rate of annual dividend = 15%
(i) Total amount of dividend paid by the company = \( \text{Total shares} \times \text{Face Value per share} \times \text{Rate of Dividend} \)
= \( 4000 \times 110 \times \frac{15}{100} = Rs. 66000 \)
(ii) Shah Rukh holds 88 shares.
Nominal value of Shah Rukh's shares = \( 88 \times 110 = Rs. 9680 \)
Annual income of Shah Rukh (dividend) = \( \text{Nominal Value of Shah Rukh's shares} \times \text{Rate of Dividend} \)
= \( 9680 \times \frac{15}{100} = Rs. 1452 \)
(iii) Shah Rukh received 10% on his investment.
Let the price Shah Rukh paid for each share (market value) be Rs. \( x \).
Total investment by Shah Rukh = \( 88 \times x \)
Annual income = Rs. 1452 (from part ii)
Rate of return on investment = \( \frac{\text{Annual Income}}{\text{Total Investment}} \times 100 \)
\( 10 = \frac{1452}{88 \times x} \times 100 \)
\( 10 \times 88 \times x = 145200 \)
\( 880x = 145200 \)
\( x = \frac{145200}{880} = Rs. 165 \)
So, Shah Rukh paid Rs. 165 for each share.
In simple words: This problem shows how to calculate dividend for a whole company and for an individual investor. We also learn how to figure out the original share price an investor paid if we know their percentage return. This helps understand company profit distribution and individual investment value.

🎯 Exam Tip: When working backwards from a percentage return to find an unknown market price, set up an equation where the dividend (income) divided by the total investment equals the given percentage return.

Question 10. What sum should Ashok invest in 25 shares selling at Rs. 36 to obtain an income of Rs. 720, if the dividend declared is 12%. Also find :
(i) the number of shares bought by Ashok.
(ii) the percentage return on his investment. Give your answer correct to the nearest whole number.
Answer:
Let's assume "25 shares" means the face value of each share is Rs. 25, as this is consistent with the solution.
Face value of each share = Rs. 25
Market value = Rs. 36
Desired total income (dividend) = Rs. 720
Rate of dividend = 12%
First, find the total face value needed to generate Rs. 720 dividend:
Total Income = \( \frac{\text{Total Face Value} \times \text{Rate of Dividend}}{100} \)
\( 720 = \frac{\text{Total Face Value} \times 12}{100} \)
Total Face Value = \( \frac{720 \times 100}{12} = Rs. 6000 \)
(i) Number of shares bought by Ashok = \( \frac{\text{Total Face Value}}{\text{Face Value per share}} = \frac{6000}{25} = 240 \) shares.
Now, calculate the total investment needed:
Investment by Ashok = \( \text{Number of shares} \times \text{Market Value per share} \)
= \( 240 \times 36 = Rs. 8640 \)
(ii) Percentage return on his investment = \( \frac{\text{Total Income}}{\text{Total Investment}} \times 100 \)
= \( \frac{720}{8640} \times 100 = 8.333...\% \)
Correct to the nearest whole number, the percentage return is 8%.
In simple words: To find out how much money Ashok needs to invest, we first figure out the total value of shares (at their face price) he needs to earn his desired income. Then, we use the actual market price to find the total investment. Finally, we calculate the percentage profit he makes on his actual investment. This helps in financial planning.

🎯 Exam Tip: Pay close attention to whether the question asks for income based on face value or return based on market value. Always round as specified in the question, or to two decimal places if not specified.

Question 11. Mr. Sharma has 60 shares of nominal value Rs. 100 and he 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, paying 18% dividend annually. Calculate:
(i) the sale proceeds.
(ii) the number of shares he buys.
(iii) the annual dividend from these shares.
Answer:
Initial shares: Number of shares = 60, Nominal value (Face value) = Rs. 100
Selling condition: 60% premium
Market value per share (at selling) = \( \text{Rs. } 100 + (60\% \text{ of Rs. } 100) = \text{Rs. } 100 + 60 = \text{Rs. } 160 \)
(i) Sale proceeds = \( \text{Number of shares} \times \text{Market value per share} \)
= \( 60 \times 160 = Rs. 9600 \)
Mr. Sharma invests these proceeds (Rs. 9600) into new shares.
New shares: Nominal value = Rs. 50, Quoted at 4% discount, Annual dividend = 18%
Market value per share (at buying) = \( \text{Rs. } 50 - (4\% \text{ of Rs. } 50) = \text{Rs. } 50 - \frac{50 \times 4}{100} = \text{Rs. } 50 - 2 = \text{Rs. } 48 \)
(ii) Number of new shares purchased = \( \frac{\text{Investment (Sale proceeds)}}{\text{Market Value per new share}} = \frac{9600}{48} = 200 \) shares.
(iii) Annual dividend from these new shares:
Total nominal value of new shares = \( 200 \times 50 = Rs. 10000 \)
Annual dividend = \( \text{Total Nominal Value} \times \text{Rate of Dividend} \)
= \( 10000 \times \frac{18}{100} = Rs. 1800 \)
In simple words: First, we calculate the total money Mr. Sharma got from selling his old shares. Then, he uses this money to buy new shares, so we find out how many new shares he can afford. Finally, we calculate the yearly income he will get from these new shares. This shows how to manage money across different stock transactions.

🎯 Exam Tip: Remember that "proceeds" refers to the money received from selling. A "premium" adds to the face value to get market value, while a "discount" subtracts from it.

Question 12. A man invests a sum of money in Rs. 100 shares, paying 15% dividend, quoted at 20% premium. If his annual dividend is Rs. 540, calculate:
(i) his total investment.
(ii) the rate of return on his investment.
Answer:
Face value of shares = Rs. 100
Rate of dividend = 15%
Shares are quoted at 20% premium.
Market value of each share = \( \text{Rs. } 100 + (20\% \text{ of Rs. } 100) = \text{Rs. } 100 + 20 = \text{Rs. } 120 \)
Annual dividend received = Rs. 540
First, find the total face value of shares required to yield Rs. 540 dividend:
Annual Dividend = \( \frac{\text{Total Face Value} \times \text{Rate of Dividend}}{100} \)
\( 540 = \frac{\text{Total Face Value} \times 15}{100} \)
Total Face Value = \( \frac{540 \times 100}{15} = Rs. 3600 \)
Number of shares = \( \frac{\text{Total Face Value}}{\text{Face Value per share}} = \frac{3600}{100} = 36 \) shares.
(i) Total investment = \( \text{Number of shares} \times \text{Market Value per share} \)
= \( 36 \times 120 = Rs. 4320 \)
(ii) Rate of return on his investment = \( \frac{\text{Annual Dividend}}{\text{Total Investment}} \times 100 \)
= \( \frac{540}{4320} \times 100 = 12.5\% \)
In simple words: We first calculate the total face value needed to get the stated dividend. This helps us find the number of shares. Then, we use the market price to determine the total money invested. Finally, we calculate the percentage profit on the actual money spent. This helps to understand the real gain from the investment.

🎯 Exam Tip: When given the annual dividend and the dividend rate, always work backwards to find the total face value of shares first, before calculating the number of shares or total investment.

Question 13. A man invests Rs. 9600 on Rs. 100 shares at Rs. 80. If the company pays him 18% dividend, find :
(i) the number of shares he buys.
(ii) his total dividend.
(iii) his percentage return on the shares.
Answer:
Amount of investment = Rs. 9600
Face value of each share = Rs. 100
Price of one share (Market value) = Rs. 80
Rate of dividend = 18%
(i) Number of shares he buys = \( \frac{\text{Amount of Investment}}{\text{Price of one share}} = \frac{9600}{80} = 120 \) shares.
(ii) To find his total dividend, first calculate the total face value of the shares:
Total face value of 120 shares = \( 120 \times 100 = Rs. 12000 \)
Total dividend = \( \text{Total Face Value} \times \text{Rate of Dividend} \)
= \( 12000 \times \frac{18}{100} = Rs. 2160 \)
(iii) His percentage return on the shares = \( \frac{\text{Total Dividend}}{\text{Amount of Investment}} \times 100 \)
= \( \frac{2160}{9600} \times 100 = 22.5\% \)
In simple words: We first calculate how many shares were bought using the investment amount and the share price. Then, we find the total yearly income (dividend) based on the face value of these shares. Finally, we determine the percentage profit made on the actual money invested. This process clarifies the direct financial outcomes of the investment.

🎯 Exam Tip: Remember to always use the face value for dividend calculations and the market value for calculating the number of shares or the actual investment amount.

Question 14. 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 Salman buys = 50
Face value (F.V.) of each share = Rs. 100
Market value (M.V.) of each share = Rs. 132
(i) Salman's investment = \( \text{Number of shares} \times \text{Market Value per share} \)
= \( 50 \times 132 = Rs. 6600 \)
(ii) Rate of dividend = 7.5%
Total face value of 50 shares = \( 50 \times 100 = Rs. 5000 \)
Annual income (dividend) = \( \text{Total Face Value} \times \text{Rate of Dividend} \)
= \( 5000 \times \frac{7.5}{100} = Rs. 375 \)
(iii) Desired extra income = Rs. 150
New target annual income = \( \text{Current annual income} + \text{Desired extra income} \)
= \( \text{Rs. } 375 + \text{Rs. } 150 = \text{Rs. } 525 \)
Let the new total number of shares be \( N \).
New target annual income = \( N \times \text{Face Value per share} \times \text{Rate of Dividend} \)
\( 525 = N \times 100 \times \frac{7.5}{100} \)
\( 525 = N \times 7.5 \)
\( N = \frac{525}{7.5} = 70 \) shares.
Extra shares Salman should buy = \( \text{New total shares} - \text{Current shares} \)
= \( 70 - 50 = 20 \) shares.
In simple words: We first calculate the total money Salman invested. Then we find his current yearly income from those shares. Finally, we figure out how many more shares he needs to buy to reach his income goal. This illustrates how to adjust an investment to meet financial targets.

🎯 Exam Tip: When increasing income, remember that the dividend rate and face value remain constant, only the number of shares changes. Work with the desired total income to find the new number of shares needed.

Question 15. 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:
Nominal value (Face value) of each share = Rs. 50
Rate of dividend = 15%
Shares are quoted at 20% premium.
Market value of each share = \( \text{Rs. } 50 + (20\% \text{ of Rs. } 50) = \text{Rs. } 50 + 10 = \text{Rs. } 60 \)
Annual dividend received = Rs. 600
Dividend per share (based on face value) = \( \text{Face Value} \times \text{Rate of Dividend} \)
= \( 50 \times \frac{15}{100} = Rs. 7.50 \)
(i) Number of shares he bought = \( \frac{\text{Total Annual Dividend}}{\text{Dividend per share}} = \frac{600}{7.50} = 80 \) shares.
(ii) His total investment = \( \text{Number of shares} \times \text{Market Value per share} \)
= \( 80 \times 60 = Rs. 4800 \)
(iii) The rate of return on his investment = \( \frac{\text{Total Annual Dividend}}{\text{Total Investment}} \times 100 \)
= \( \frac{600}{4800} \times 100 = 12.5\% \)
In simple words: First, we find out how much dividend each share pays. Then, we use the total dividend Salman received to calculate how many shares he bought. After that, we figure out his total investment based on the market price. Finally, we see what percentage of his invested money he got back. This helps understand the efficiency of the investment.

🎯 Exam Tip: Be careful to calculate dividend per share based on face value, and then use the market value to determine the total investment. These are distinct concepts in share calculations.

Question 16. 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:
Rohit's initial investment = Rs. 9600
Face value of initial shares = Rs. 100
Market value of initial shares = \( \text{Rs. } 100 + \text{Rs. } 20 \text{ (premium)} = \text{Rs. } 120 \)
Dividend rate (first case) = 8%
(i) Original number of shares = \( \frac{\text{Initial Investment}}{\text{Market Value per share}} = \frac{9600}{120} = 80 \) shares.
Rohit sold these 80 shares when the price rose to Rs. 160 each.
(ii) Sale proceeds = \( \text{Number of shares} \times \text{Selling Price per share} \)
= \( 80 \times 160 = Rs. 12800 \)
Rohit invested these sale proceeds (Rs. 12800) into new shares.
New shares: Face value = Rs. 50, Market value = Rs. 40, Dividend rate = 10%
(iii) New number of shares = \( \frac{\text{Investment (Sale proceeds)}}{\text{Market Value per new share}} = \frac{12800}{40} = 320 \) shares.
(iv) Calculate the dividend for both cases:
Dividend (first case):
Total face value of original shares = \( 80 \times 100 = Rs. 8000 \)
Dividend (first case) = \( 8000 \times \frac{8}{100} = Rs. 640 \)
Dividend (second case):
Total face value of new shares = \( 320 \times 50 = Rs. 16000 \)
Dividend (second case) = \( 16000 \times \frac{10}{100} = Rs. 1600 \)
Change in the two dividends = \( \text{Dividend (second case)} - \text{Dividend (first case)} \)
= \( \text{Rs. } 1600 - \text{Rs. } 640 = \text{Rs. } 960 \)
In simple words: This problem involves two stages of investment. First, we find how many shares Rohit bought, then how much money he got when he sold them. Next, he uses that money to buy new shares, so we find the number of new shares. Finally, we compare the income from dividends in both situations to see the change. This shows the results of re-investing profits.

🎯 Exam Tip: Clearly separate calculations for the first and second investments. Note that "proceeds (excluding dividend)" means the dividend from the first investment is not added to the capital for the second investment.

Question 17. Ashok invested Rs. 26,400 on 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:
Ashok's total investment = Rs. 26400
Rate of dividend = 12%
Face value of one share = Rs. 25
Total dividend received = Rs. 2475
The total dividend is calculated using the number of shares, face value, and dividend rate:
Total Dividend = \( \text{Number of Shares} \times \text{Face Value per share} \times \text{Rate of Dividend} \)
\( 2475 = \text{Number of Shares} \times 25 \times \frac{12}{100} \)
\( 2475 = \text{Number of Shares} \times 3 \)
(i) Number of shares he bought = \( \frac{2475}{3} = 825 \) shares.
(ii) The market value of each share is found by dividing the total investment by the number of shares bought:
Market value of each share = \( \frac{\text{Total Investment}}{\text{Number of Shares bought}} \)
= \( \frac{26400}{825} = Rs. 32 \)
In simple words: First, we use the total dividend, dividend rate, and face value to figure out how many shares Ashok bought. Then, we divide his total investment by the number of shares to find the actual price he paid for each share. This helps determine the quantity of shares and their individual cost.

🎯 Exam Tip: Remember that dividend received is directly proportional to the number of shares and their face value. Use this relationship to find unknowns like the number of shares first.