Frank Brothers Solutions for ICSE Class 10 Mathematics Chapter 4 Shares and Dividends

Exercise 4.1

Answer 1.
a) 500 shares of Rs 75 each at a premium of Rs 17.
No. of shares to be purchased = 500
Rs 75 shares at a premium of Rs 17 = Rs (75+17) = Rs 92
Therefore, money required to purchase 500 shares = Rs 92 × 500 = Rs 46,000.

b) 315 shares of Rs 60 each at a premium of Rs 12.
No. of shares to be purchased = 315
Rs 60 shares at a premium of Rs 12 = Rs (60+12) = Rs 72
Therefore, money required to purchase 315 shares = Rs 72 × 315 = Rs 22,680.

c) 600 shares of Rs 25 each at a discount of Rs 3.
No. of shares to be purchased = 600
Rs 25 shares at a discount of Rs 3 = Rs (25-3) = Rs 22
Therefore, money required to purchase 600 shares = Rs 22 × 600 = Rs 13,200.

d) 425 shares of Rs 10 each at a discount of Rs 1.50.
No. of shares to be purchased = 425
Rs 10 shares at a discount of Rs 1.50 = Rs (10-1.50) = Rs 8.50
Therefore, money required to purchase 425 shares = Rs 8.50 × 425 = Rs 3,612.50.

e) 250 shares of Rs 20 each at par.
No. of shares to be purchased = 250
Cost of each share = Rs 20
Therefore, money required to purchase 250 shares = Rs 20 × 250 = Rs 5,000.

f) 150 shares of Rs 100 each at a premium of 12%.
No. of shares to be purchased = 150
Rs 100 shares at a premium of 12% = Rs (100+12% of Rs 100) = Rs (100+12) = Rs 112
Therefore, money required to purchase 150 shares = Rs 112 × 150 = Rs 16,800.

g) 220 shares of Rs 75 each at a premium of 15%.
No. of shares to be purchased = 220
Rs 75 shares at a premium of 15% = Rs (75+15% of Rs 75) = Rs (75+11.25) = Rs 86.25
Therefore, money required to purchase 220 shares = Rs 86.25 × 220 = Rs 18,975.

h) 340 shares of Rs 125 each at a discount of 20%.
No. of shares to be purchased = 340
Rs 125 shares at a discount of 20% = Rs (125 - 20% of Rs 125) = Rs(125 - 25) = Rs 100
Therefore, money required to purchase 340 shares = Rs 100 × 340 = Rs 34,000.

i) 750 shares of Rs 100 each at a discount of 24%.
No. of shares to be purchased = 750
Rs 100 shares at a discount of 24% = Rs (100 - 24% of Rs 100) = Rs(100 - 24) = Rs 76
Therefore, money required to purchase 750 shares = Rs 76 × 750 = Rs 57,000.

j) 116 shares of Rs 125 each at par.
No. of shares to be purchased = 116
Cost of each share = Rs 125
Therefore, money required to purchase 116 shares = Rs 125 × 116 = Rs 14,500.
In simple words: When you buy shares at premium, you pay more than face value. At discount, you pay less. At par means you pay exactly the face value.

📝 Teacher's Note: Show students examples with real money. If a chocolate costs Rs 10 but you pay Rs 12, that's premium. If you pay Rs 8, that's discount. Same idea with shares.

🎯 Exam Tip: For premium, add the extra amount. For discount, subtract. Always multiply the final price per share with number of shares to get total investment.

Answer 2.
a) 180 shares of Rs 50 each paying 12% dividend.
No. of shares = 180
Price of each share = Rs 50
Therefore, Total investment = Rs (50 × 180) = Rs 9,000
Dividend = 12%
Hence Annual Income = Rs \( \frac{12 × 9,000}{100} \) = Rs 1,080

b) 424 shares of Rs 125 each paying 8% dividend.
No. of shares = 424
Price of each share = Rs 125
Therefore, Total investment = Rs (125 × 424) = Rs 53,000
Dividend = 8%
Hence Annual Income = Rs \( \frac{8 × 53,000}{100} \) = Rs 4,240

c) 60 shares of Rs 100 each available at Rs 75 and paying 5% dividend.
No. of shares = 60
Price of each share = Rs 100
Face value of 60 shares = Rs(100 × 60) = Rs 6,000
Dividend = 5%
Therefore, Annual Income = Rs \( \frac{5 × 6,000}{100} \) = Rs 300

d) 120 shares of Rs 50 each available at Rs 62 and paying 13% dividend.
No. of shares = 120
Price of each share = Rs 50
Face value of 120 shares = Rs(50 × 120) = Rs 6,000
Dividend = 13%
Therefore, Annual Income = Rs \( \frac{13 × 6,000}{100} \) = Rs 780.
In simple words: Dividend is always calculated on face value of shares, not on the price you paid. It's like interest on the original value of the share.

📝 Teacher's Note: Students often confuse market price with face value. Dividend is always on face value. Use bank deposit example - interest is on deposit amount, not withdrawal amount.

🎯 Exam Tip: Write formula: Annual Income = (Dividend % × Face value × Number of shares) ÷ 100. Always use face value, not market price.

Answer 3.
a) Rs 7,225 paying 12% when a Rs 100 share is available at 15% discount.
Investment = Rs 7,225
Nominal value of each share = Rs 100
Market value = Rs(100 - 15% of Rs 100) = Rs (100-15) = Rs 85
No. of shares purchased = \( \frac{7,225}{85} \) = 85
Face value of 85 shares = Rs 100 × 85 = Rs 8,500
Dividend = 12%
Therefore, Annual Income = \( \frac{12 × 8,500}{100} \) = Rs 1,020
Hence, percentage income = \( \frac{1,020 × 100}{7,225} \) = 14.117% = 14.12%

b) Rs 7,168 paying 15% when a Rs 80 share is available at 40% premium.
Investment = Rs 7,168
Nominal value of each share = Rs 80
Market value = Rs(80 + 40% of Rs 80) = Rs (80+32) = Rs 112
No. of shares purchased = \( \frac{7,168}{112} \) = 64
Face value of 64 shares = Rs 80 × 64 = Rs 5,120
Dividend = 15%
Therefore, Annual Income = \( \frac{15 × 5,120}{100} \) = Rs 768
Hence, percentage income = \( \frac{768 × 100}{7,168} \) = 10.71%

c) Rs 36,250 in a Rs 125 share paying 8% and available at a premium of Rs 20.
Investment = Rs 36,250
Nominal value of each share = Rs 125
Market value = Rs (125 + Rs 20) = Rs 145
No. of shares purchased = \( \frac{36,250}{145} \) = 250
Face value of 250 shares = Rs 125 × 250 = Rs 31,250
Dividend = 8%
Therefore, Annual Income = \( \frac{8 × 31,250}{100} \) = Rs 2,500
Hence, percentage income = \( \frac{2,500 × 100}{36,250} \) = 6.9%

d) Rs 12,375 in a Rs 75 share paying 4% and available at a discount of Rs 20.
Investment = Rs 12,375
Nominal value of each share = Rs 75
Market value = Rs (75 - Rs 20) = Rs 55
No. of shares purchased = \( \frac{12,375}{55} \) = 225
Face value of 225 shares = Rs 75 × 225 = Rs 16,875
Dividend = 4%
Therefore, Annual Income = \( \frac{4 × 16,875}{100} \) = Rs 675
Hence, percentage income = \( \frac{675 × 100}{12,375} \) = 5.45%
In simple words: Percentage income tells you how much return you get on the money you actually spent. It's like finding the profit percentage on your investment.

📝 Teacher's Note: Percentage income = (Annual Income ÷ Actual Investment) × 100. Students should remember that dividend is on face value but percentage return is on investment made.

🎯 Exam Tip: First find annual income using face value. Then divide by actual investment and multiply by 100 for percentage. Show both steps clearly.

Answer 4.
No. of shares = 500
Nominal value of each share = Rs 125
Face value of 500 shares = Rs (125 × 500) = Rs 62,500
Rate of dividend = 12%
Total dividend = \( \frac{62500 × 12}{100} \) = Rs 7,500
Rate of income tax = 5%
Total tax = \( \frac{5 × 7,500}{100} \) = Rs 375
Net income = Rs (7,500 - 375) = Rs 7,125
In simple words: When you get dividend, you have to pay tax on it. Net income is what you get after paying the tax to the government.

📝 Teacher's Note: Just like salary has tax deduction, dividend income also has tax. Net income = Gross dividend - Tax paid. Use simple salary example to explain this.

🎯 Exam Tip: Calculate total dividend first. Then find tax amount. Subtract tax from dividend to get net income. Show all three steps clearly in the answer.

Answer 5.
Answer:
No. of shares = 1200
Nominal value of each share = Rs 150

Face value of 1200 shares = Rs (150 × 1200) = Rs 1,80,000

Rate of dividend = 18%

Total dividend = \( \frac{1,80,000 \times 18}{100} \) = Rs 32,400

Rate of income tax = 8%

Total tax = \( \frac{8 \times 32,400}{100} \) = Rs 2,592

Net income = Rs (32,400 - 2,592) = Rs 29,808

In simple words: First we find how much dividend money the person gets. Then we take out the tax from that. What is left is the net income.

📝 Teacher's Note: Teach students that dividend is always calculated on face value, not market value. Also show that income tax reduces the final amount they receive.

🎯 Exam Tip: Always calculate dividend first, then tax, then subtract to get net income. Write all steps clearly with the right formula.

Answer 6.
Answer:
No. of shares = 750
Nominal value of each share = Rs 60

Face value of 750 shares = Rs (60 × 750) = Rs 45,000

Rate of dividend = 15%

Total dividend = \( \frac{45,000 \times 15}{100} \) = Rs 6,750

Rate of income tax = 6%

Total tax = \( \frac{6 \times 6,750}{100} \) = Rs 405

Net income = Rs (6,750 - 405) = Rs 6,345

In simple words: The person gets Rs 6,750 as dividend. Then he pays Rs 405 as tax. So he keeps Rs 6,345 as his final income.

📝 Teacher's Note: Make students practice the three-step process: find dividend amount, find tax amount, subtract tax from dividend. Use simple examples with round numbers first.

🎯 Exam Tip: Remember that tax is calculated on the dividend amount, not on the total investment. Show this calculation step clearly.

Answer 7.
Answer:
No. of shares = 600
Nominal value of a share = Rs 50
Investment by Mahesh = Rs (50 × 600) = Rs 30,000

Shares sold at premium = \( \frac{1}{3} \times 600 \) = 200

Market value of a share with Premium = Rs (50 + 20) = Rs 70

Value of 200 shares = Rs (70 × 200) = Rs 14,000 ............(i)

Shares sold at discount = 600 - 200 = 400

Market value of a share with discount = Rs (50 - 5) = Rs 45

Value of 400 shares = Rs (45 × 400) = Rs 18,000 ............(ii)

Adding (i) and (ii), gives total money Mahesh received by selling his shares = Rs (14,000 + 18,000) = Rs 32,000
Difference in selling price and cost price = Rs (32,000 - 30,000) = Rs 2,000
Hence, Mahesh gained Rs 2,000

In simple words: Mahesh bought shares for Rs 30,000. He sold them for Rs 32,000. So he made a profit of Rs 2,000.

📝 Teacher's Note: Explain that premium means selling above face value and discount means selling below face value. Use examples like selling a Rs 100 item for Rs 120 (premium) or Rs 80 (discount).

🎯 Exam Tip: Always find the total cost first, then total selling price. The difference gives profit or loss. Label each calculation clearly.

Answer 8.
Answer:
Investment by Divya = Rs 50,000
Nominal value of a share = Rs 125

No. of shares purchased by Divya = \( \frac{50,000}{125} \) = 400

Shares sold at premium = 200

Market value of a share with Premium = Rs (125 + 24% of Rs 125)
= Rs (125 + 30) = Rs 155

Value of 200 shares = Rs (155 × 200) = Rs 31,000 ............(i)

Shares sold at discount = 200

Market value of a share with discount = Rs (125 - 20% of Rs 125)
= Rs (125 - 25) = Rs 100

Value of 200 shares = Rs (100 × 200) = Rs 20,000 ............(ii)

Adding (i) and (ii), gives total money Divya received by selling her shares = Rs (31,000 + 20,000) = Rs 51,000
Hence, Divya gained Rs 1,000

In simple words: Divya bought shares for Rs 50,000. She sold them for Rs 51,000. So she made a profit of Rs 1,000.

📝 Teacher's Note: Show students how to calculate percentage of a number. 24% of Rs 125 means (24/100) × 125. Practice this calculation separately.

🎯 Exam Tip: When the problem gives percentages for premium or discount, convert them to actual rupee amounts first. Then proceed with normal calculations.

Answer 9.
Answer:
Investment by Ashutosh = Rs 58,500

Price at which Ashutosh purchased one share = Rs (150 + 30% of Rs 150) = Rs (150 + 45) = Rs 195

No. of shares purchased by Ashutosh = \( \frac{58,500}{195} \) = 300

Shares sold at Rs 215 = 1/3 × 300 = 100

Selling price of 100 shares at Rs 215 = Rs (100 × 215) = Rs 21,500 ...........(i)

Shares sold at Rs 195 = 1/3 × 300 = 100
Selling price of 100 shares at Rs 175 = Rs (100 × 175) = Rs 17,500 ...........(iii)

Adding (i), (ii) and (iii), gives total money Ashutosh received by selling his shares = Rs (21,500 + 19,500 + 17,500) = Rs 58,500

Difference in selling price and cost price = Rs (58,500 - 58,500) = Rs 0.
Hence, Ashutosh sold his shares at no loss or no gain.

In simple words: Ashutosh bought shares for Rs 58,500. He sold them for exactly Rs 58,500. So he made no profit and no loss.

📝 Teacher's Note: This is a special case where selling price equals cost price. Explain that this means "break-even" - no profit, no loss. Students should understand this concept.

🎯 Exam Tip: When the difference between cost and selling price is zero, always write "no profit, no loss" or "break-even". This is the exact answer examiners want.

Ex 4.2

Answer 1.
Answer:
Let total savings be x.

Investment in company A = 10% of x = \( \frac{10}{100} \times x = \frac{x}{10} \)

Investment in company B = 30% of x = \( \frac{30}{100} \times x = \frac{3x}{10} \)

Investment in company C = 40% of x = \( \frac{40}{100} \times x = \frac{4x}{10} = \frac{2x}{5} \)

Dividend given by company A = 12% of \( \frac{x}{10} \)
= \( \frac{12 \times x}{100 \times 10} \) = 0.012x ..........(i)

Dividend given by company B = 15% of \( \frac{3x}{10} \)
= \( \frac{15 \times 3x}{100 \times 10} \) = 0.045x ..........(ii)

Dividend given by company C = 16% of \( \frac{2x}{5} \)
= \( \frac{16 \times 2x}{100 \times 5} \) = 0.064x ............(iii)

(i) + (ii) + (iii) = Rs 3,025 ...........(given)

(0.012 + 0.045 + 0.064)x = Rs 3,025

0.121x = Rs 3,025

x = Rs \( \frac{3,025}{0.121} \) = Rs 25,000

Hence, Saurav's savings = Rs 25,000

Investment in company A = Rs \( \frac{x}{10} \) = Rs \( \frac{25,000}{10} \) = Rs 2,500

Investment in company B = Rs \( \frac{3x}{10} \) = Rs \( \frac{75,000}{10} \) = Rs 7,500

Investment in company C = Rs \( \frac{2x}{5} \) = Rs \( \frac{50,000}{5} \) = Rs 10,000

In simple words: We use algebra to find the total savings. We know the dividend percentages and the total dividend amount. From this we work backwards to find how much money was invested.

📝 Teacher's Note: This is a reverse problem. Instead of finding dividend from investment, we find investment from dividend. Teach students to set up the equation carefully.

🎯 Exam Tip: Always convert percentages to decimals when adding them. Then solve the simple equation. Show all investment amounts at the end as the final answer.

Answer 2.
Answer:
Let total savings be x.

Investment in 'Infosys' = 15% of x = \( \frac{15}{100} \times x = \frac{3x}{20} \)

Investment in 'Wipro' = 25% of x = \( \frac{25}{100} \times x = \frac{x}{4} \)

Investment in 'Reliance' = 35% of x = \( \frac{35}{100} \times x = \frac{7x}{20} \)

Dividend given by 'Infosys' = 16% of \( \frac{3x}{20} \)
= \( \frac{16 \times 3x}{100 \times 20} = 0.024x \).........(i)

Dividend given by 'Wipro' = 18% of \( \frac{x}{4} \)
= \( \frac{18 \times x}{100 \times 4} = 0.045x \).........(ii)

Dividend given by 'Reliance' = 20% of \( \frac{7x}{20} \)
= \( \frac{20 \times 7x}{100 \times 20} = 0.07x \).........(iii)

(i) + (ii) + (iii) = Rs 52,125 .........(given)

(0.024 + 0.045 + 0.07)x = Rs 52,125

0.139x = Rs 52,125

x = Rs \( \frac{52,125}{0.139} \) = Rs3,75,000

Hence, Akanksha's savings = Rs 3,75,000

Investment in 'Infosys' = Rs \( \frac{3x}{20} = Rs \frac{3 \times 3,75,000}{20} \) = Rs56,250

Investment in 'Wipro' = Rs \( \frac{x}{4} = Rs \frac{3,75,000}{4} \) = Rs93,750

Investment in 'Reliance' = Rs \( \frac{7x}{20} = Rs \frac{7 \times 3,75,000}{20} \) = Rs1,31,250

In simple words: We found total savings by adding all three dividend amounts and working backward using percentages. Then we calculated each company investment amount.

📝 Teacher's Note: Help students understand that we use algebra here. Let x be the unknown total. Each investment is a percentage of x. All dividend amounts add up to Rs 52,125.

🎯 Exam Tip: Always write "Let total savings be x" first. Show each step clearly. Check your final answer by verifying that all percentages add up correctly.

Answer 3.
Answer:
Total investment = Rs (24,000+30,000) = Rs 54,000

No. of shares of 'Vam Organics' = \( \frac{\text{money invested}}{\text{cost of one share}} = \frac{24,000}{100} \) = 240

No. of shares of 'Hero Honda' = \( \frac{\text{money invested}}{\text{cost of one share}} = \frac{30,000}{100} \) = 300

Dividend given by 'Vam Organics' = 12% = Rs \( \frac{12 \times 24,000}{100} \) = Rs2,880

Dividend given by 'Hero Honda' = 15% = Rs \( \frac{15 \times 30,000}{100} \) = Rs4,500

Total dividend earned = Rs (2,880+4,500) = Rs 7,380

Money earned by selling shares of 'Vam Organics' = Rs (95 × 240)
= Rs 22,800

Money earned by selling shares of 'Hero Honda' = Rs (90 × 300)
= Rs 27,000

Total money earned by selling shares = Rs (22,800+27,000) = Rs 49,800

Total earnings = money earned by selling shares + dividends earned
= Rs (49,800+7,380) = Rs 57,180

Tarun's earnings from the transactions = Rs (57,180-54,000)
= Rs 3,180

In simple words: Tarun bought shares, got dividends, then sold shares. His total profit is all money received minus what he originally spent.

📝 Teacher's Note: Explain that profit from shares comes in two ways - dividends (regular payments) and capital gains (selling price minus buying price). Both must be added together.

🎯 Exam Tip: Always calculate total earnings first, then subtract total investment to get profit. Show all steps clearly. Remember to include both dividend income and selling income.

Answer 4.
Answer:
Total investment = Rs (20,000+25,000) = Rs 45,000

Dividend given by 'Bharati Telecom' = 10% = Rs \( \frac{10 \times 20,000}{100} \) = Rs2,000

Dividend given by 'Satyam Infoways' = 12.5% =
Rs \( \frac{12.5 \times 25,000}{100} = Rs \frac{125 \times 25,000}{10 \times 100} \) = Rs3,125

Total dividend earned = Rs (2,000+3,125) = Rs 5,125

Money earned by selling shares of 'Bharati Telecom'
= Rs (20,000 – 4% of Rs 20,000)= Rs (20,000-800) = Rs 19,200

Money earned by selling shares of 'Satyam Infoways'
= Rs (25,000 – 5% of Rs 25,000) = Rs (25,000 – 1250) = Rs 23,750

Total money earned by selling shares = Rs (19,200+23,750) = Rs 42,950

Total earnings = money earned by selling shares + dividends earned = Rs (42,950+5,125) = Rs 48,075

Bhavana's earnings from the transactions = Rs (48,075-45,000)
= Rs 3,075

In simple words: Bhavana bought shares worth Rs 45,000. She got dividends and then sold shares at a loss. But her total dividends were more than the loss, so she made a small profit.

📝 Teacher's Note: Point out that even when selling price is less than buying price, dividends can still make the investment profitable. This is why dividend income is important.

🎯 Exam Tip: When shares are sold at a loss (4% less, 5% less), calculate the actual selling amount carefully. Don't forget to add dividend income to get total earnings.

Answer 5.
Answer:
Let Karan's investment be x.

Face value of 125 shares = Rs (100 × 125) = Rs 12,500

Dividend for 125 shares = 6% of 12,500 = Rs \( \frac{6 \times 12,500}{100} \) = Rs750

He gets Rs 750 as dividend which is equal to 4% of money invested

\( \implies \frac{4x}{100} \) = Rs750
\( \implies \) 4x = Rs75,000
\( \implies \) x = Rs \( \frac{75,000}{4} \)
\( \implies \) x = Rs18,750

Hence, Karan invested Rs 18,750.

No. of shares bought by Karan = 125

Value of a share = Rs \( \frac{18,750}{125} \) = Rs150

Karan bought a share for Rs 150.

In simple words: We know the dividend amount and that it equals 4% of investment. We worked backward to find the total investment amount. Then we divided by number of shares to find price per share.

📝 Teacher's Note: Remind students that dividend is calculated on face value (Rs 100 per share), but the actual buying price can be different. Here face value is Rs 100 but buying price is Rs 150.

🎯 Exam Tip: Set up the equation "dividend = 4% of investment" carefully. Show that face value and market value are different. Always find market value per share at the end.

Answer 6.
Answer:
Let Vikram's investment be x.

Face value of 200 shares = Rs (25 × 200) = Rs 5,000

Dividend for 200 shares = 8% of Rs 5,000 = Rs \( \frac{8 \times 5,000}{100} \) = Rs400

He gets Rs 400 as dividend which is equal to 10% of money invested

\( \implies \frac{10x}{100} \) = Rs400
\( \implies \) x = Rs4,000
Hence, Vikram invested Rs 4,000.

No. of shares bought by Vikram = 200

Value of a share = Rs \( \frac{4,000}{200} \) = Rs20

Vikram bought a share for Rs 20.

In simple words: Similar to previous problem. Dividend is 8% of face value but equals 10% of actual investment. We found the actual investment, then calculated price per share.

📝 Teacher's Note: Here face value is Rs 25 per share but market price is only Rs 20. Students should see that market price can be less than face value too.

🎯 Exam Tip: Note that face value (Rs 25) is higher than market price (Rs 20). This means shares are selling at a discount. Always calculate market price per share correctly.

Answer 7.
Answer:
Let Archana's investment be x.

Face value of 250 shares = Rs (50 × 250) = Rs 12,500

Dividend for 250 shares = 12% of Rs 12,500 = Rs \( \frac{12 \times 12,500}{100} \) = Rs1,500

She gets Rs 1,500 as dividend which is equal to 15% of money invested

\( \implies \frac{15x}{100} \) = Rs1,500
\( \implies \) x = Rs10,000
Hence, Archana invested Rs 10,000.

No. of shares bought by Archana = 250

Value of a share = Rs \( \frac{10,000}{250} \) = Rs40

Archana bought a share for Rs 40.

In simple words: Same method as previous questions. Face value is Rs 50 but market price is Rs 40. Archana bought shares at a discount and got good dividend returns.

📝 Teacher's Note: Show students how to check their answer: 250 shares × Rs 40 = Rs 10,000 investment. 15% of Rs 10,000 = Rs 1,500 dividend. This matches the given information.

🎯 Exam Tip: Always verify your answer by checking if the dividend percentage of your calculated investment matches the given dividend amount. This prevents calculation errors.

Answer 8.
Answer:
a) 12% at 125 or 16% at 150

12% at 125:
Income on Rs 125 = Rs 12

Income on Re 1 = \( \frac{12}{125} \) = 0.096

16% at 150:

Income on Rs 150 = Rs 16

Income on Re 1 = \( \frac{16}{150} \) = 0.106

Therefore, 16% at 150 is a better investment.

b) 16% at 80 or 18% at 120

16% at 80:
Income on Rs 80 = Rs 16

Income on Re 1 = \( \frac{16}{80} \) = 0.20

18% at 120:

Income on Rs 120 = Rs 18

In simple words: To compare investments, we find income per rupee invested. Higher income per rupee means better investment. We divide dividend by market price to get this.

📝 Teacher's Note: Explain that "12% at 125" means 12% dividend rate and Rs 125 market price per share. Students should always calculate income per rupee to compare different investments.

🎯 Exam Tip: Use the formula: Income per rupee = Dividend rate ÷ Market price. Convert to decimal for easy comparison. Higher value means better investment.

Answer 9.
Answer:
In first case:
No. of shares sold = 350
Face value of each share = Rs 150
Face value of 350 shares = Rs (150 × 350) = Rs 52,500
Market value of each share = Rs 120
Market value of 350 shares = Rs (120 × 350) = Rs 42,000
Dividend (income) for 350 shares = 6% of Rs 52,500 = Rs \( \frac{6 \times 52,500}{100} \) = Rs 3,150

In second case:
Proceeds from selling 350 shares = Rs 42,000
Face value of each share = Rs 75
Market value of each share = Rs 75
No. of shares bought = \( \frac{42,000}{75} \) = 560
Usha bought 560 shares of Rs 75 each.
Face value of 560 shares = Rs (75 × 560) = Rs 42,000
Dividend (income) for 560 shares = 8% of Rs 42,000 = Rs \( \frac{8 \times 42,000}{100} \) = Rs 3,360
Change in annual income = Rs (3,360 - 3,150) = Rs 210
In simple words: Usha sold shares in one company and bought shares in another company. Her dividend income increased by Rs 210 because the new company gave higher dividend rate.

📝 Teacher's Note: Show students that dividend is always calculated on face value, not market value. Face value is the original price printed on the share certificate.

🎯 Exam Tip: Always calculate dividend using face value × dividend rate ÷ 100. Write each step clearly to get full marks.

Answer 10.
Answer:
In first case:
No. of shares sold = 400
Face value of each share = Rs 100
Face value of 400 shares = Rs (100 × 400) = Rs 40,000
Market value of each share = Rs 125
Market value of 400 shares = Rs (125 × 400) = Rs 50,000
Dividend (income) for 400 shares = 12.5% of Rs 40,000 = Rs \( \frac{12.5 \times 40,000}{100} \) = Rs 5,000

In second case:
Proceeds from selling 400 shares = Rs 50,000
Face value of each share = Rs 50
Market value of each share = Rs 80
No. of shares bought = \( \frac{50,000}{80} \) = 625
Amitesh bought 625 shares of Rs 80 each.
Face value of 625 shares = Rs (50 × 625) = Rs 31,250
Dividend (income) for 625 shares = 16% of Rs 31,250 = Rs \( \frac{16 \times 31,250}{100} \) = Rs 5,000
Change in annual income = Rs (5,000 - 5,000) = Rs 0 = Nil
In simple words: Amitesh sold shares and bought new shares. His dividend income stayed exactly the same because the calculations balanced out perfectly.

📝 Teacher's Note: This problem shows that sometimes when you change investments, your income can stay the same. The market price and dividend rates work together to give the same result.

🎯 Exam Tip: When change in income is zero, write "Rs 0" or "Nil". Don't leave it blank. Show all working steps to prove the answer.

Answer 11.
Answer:
In first case:
No. of shares sold = 250
Face value of each share = Rs 75
Face value of 250 shares = Rs (75 × 250) = Rs 18,750
Market value of each share = Rs 112
Market value of 250 shares = Rs (112 × 250) = Rs 28,000
Dividend (income) for 250 shares = 8% of Rs 18,750 = Rs \( \frac{8 \times 18,750}{100} \) = Rs 1,500

In second case:
Proceeds from selling 250 shares = Rs 28,000
Face value of each share = Rs 125
Market value of each share = Rs 140
No. of shares bought = \( \frac{28,000}{140} \) = 200
Mr Lele bought 200 shares of Rs 140 each.
Face value of 200 shares = Rs (125 × 200) = Rs 25,000
Dividend (income) for 200 shares = 8% of Rs 25,000 = Rs \( \frac{8 \times 25,000}{100} \) = Rs 2,000
Change in annual income = Rs (2,000 - 1,500) = Rs 500
In simple words: Mr Lele sold 250 shares and bought 200 shares in a different company. His dividend income increased by Rs 500 per year.

📝 Teacher's Note: Even though Mr Lele bought fewer shares (200 instead of 250), his income increased because the new shares had higher face value and same dividend rate.

🎯 Exam Tip: Remember to subtract old income from new income to find the change. Write "increase" or "decrease" clearly with the final answer.

Answer 12.
Answer:
In first case:
No. of shares sold = 1000
Face value of each share = Rs 125
Face value of 1000 shares = Rs (125 × 1000) = Rs 1,25,000
Market value of each share = Rs 150
Market value of 1000 shares = Rs (150 × 1000) = Rs 1,50,000
Dividend (income) for 1000 shares = 12% of Rs 1,25,000 = Rs \( \frac{12 \times 1,25,000}{100} \) = Rs 15,000

In second case:
Proceeds from selling 1000 shares = Rs 1,50,000
Face value of each share = Rs 25
Market value of each share = Rs 60
No. of shares bought = \( \frac{1,50,000}{60} \) = 2,500
Rohit bought 2,500 shares of Rs 60 each.
Face value of 2,500 shares = Rs (25 × 2,500) = Rs 62,500
Dividend (income) for 2,500 shares = 20% of Rs 62,500 = Rs \( \frac{20 \times 62,500}{100} \) = Rs 12,500
Change in annual income = Rs (12,500 - 15,000) = - Rs 2,500 (less)
In simple words: Rohit sold 1000 expensive shares and bought 2500 cheaper shares. His yearly dividend income decreased by Rs 2,500 because the new investment gives less money.

📝 Teacher's Note: Sometimes selling good shares to buy cheaper ones can reduce your income. Students should compare dividend rates carefully before making investment decisions.

🎯 Exam Tip: When income decreases, write "-Rs amount" or "Rs amount (less)". Both ways are correct. Always show the decrease clearly in your final answer.

Exercise 4.3

Answer 13.
Answer:
Given:
Let x = number of shares purchased by Mr Lal
Value of x shares = Rs (100 × x) = Rs 100x
Dividend rate = 15%
Monthly scholarship = Rs 225

Step 1: Calculate dividend from x shares.
Dividend = 15% of Rs 100x = \( \frac{15 \times 100x}{100} \) = Rs 15x

Step 2: Set up equation using monthly scholarship.
Monthly scholarship = Rs 225 = Dividend/12
\( \Rightarrow \) Rs \( \frac{15x}{12} \) = Rs 225
\( \Rightarrow \) Rs 15x = Rs 2,700
\( \Rightarrow \) x = 180

Step 3: Calculate investment amount.
Market price per share = Rs 120
Investment = Rs (120 × 180) = Rs 21,600

Therefore, Mr Lal should purchase 180 shares and invest Rs 21,600.
In simple words: Mr Lal needs monthly income of Rs 225. We worked backwards from this amount to find how many shares he needs to buy. Then we calculated the total cost.

📝 Teacher's Note: Show students that monthly income comes from yearly dividend divided by 12. This helps them understand the connection between dividend rate and monthly payments.

🎯 Exam Tip: Always write "Let x = number of shares" at the start. Show all steps clearly. Write final answer with both number of shares and total investment amount.

Answer 14.
Answer:
Given:
Let x = number of shares purchased by Gayathri
Value of x shares = Rs 75 × x = Rs 75x
Dividend rate = 20%
Monthly income = Rs 500

Step 1: Calculate dividend from x shares.
Dividend = 20% of Rs 75x = \( \frac{20 \times 75x}{100} \) = Rs 15x

Step 2: Set up equation using monthly income.
Monthly income = Rs 500 = Dividend/12
\( \Rightarrow \) Rs \( \frac{15x}{12} \) = Rs 500
\( \Rightarrow \) Rs 15x = Rs 6,000
\( \Rightarrow \) x = 400

Step 3: Calculate investment amount.
Market price per share = Rs 62.50
Investment = Rs (62.50 × 400) = Rs 25,000

Therefore, Gayathri should purchase 400 shares and invest Rs 25,000.
In simple words: Gayathri wants Rs 500 per month. We found she needs 400 shares to get this income. The total cost to buy these shares is Rs 25,000.

📝 Teacher's Note: Remind students that dividend is calculated on face value (Rs 75), not market value (Rs 62.50). This is a common mistake students make.

🎯 Exam Tip: Remember: dividend is always on face value. Investment calculation uses market value. These are different amounts - do not confuse them.

Answer 1.
Answer:
For shares of 'Bihar Steel':
Let x = number of shares sold by Ramesh
Nominal value of each share = Rs 100
Face value of x shares = Rs 100x
Market value of each share = Rs 130
Market value of x shares = Rs 130x = proceeds from selling

Dividend = 8% of Rs 100x = \( \frac{8}{100} \times \) Rs 100x = Rs 8x .........(i)

For shares of 'Jindal Steel':
Market value of each share = Rs 75
Number of shares bought = \( \frac{\text{proceeds from selling 'Bihar steel'}}{\text{market value of 'Jindal steel'}} \) = \( \frac{130x}{75} \)

Nominal value of each share = Rs 50
Face value of \( \frac{130x}{75} \) shares = Rs 50 × \( \frac{130x}{75} \) = Rs 86.667x

Dividend = 12% of Rs 86.667x = Rs \( \frac{12 \times 86.667x}{100} \) = Rs 10.40x .....(ii)

Step 1: Calculate increase in annual income.
Increase in annual income = Rs 360 = subtraction of (i) from (ii)
Rs (10.40x - 8x) = Rs 360
\( \Rightarrow \) 2.4x = Rs 360
\( \Rightarrow \) x = 150

Therefore, Ramesh sold 150 shares.
In simple words: Ramesh sold Bihar Steel shares and bought Jindal Steel shares with that money. The new shares give him Rs 360 more income per year. We worked backwards to find how many shares he sold.

📝 Teacher's Note: Show students to first calculate dividend from old shares, then dividend from new shares. The difference gives the increase in income. Use this to find the unknown.

🎯 Exam Tip: Write equations (i) and (ii) clearly. Show that increase = (ii) - (i). Always check your final answer by substituting back.

Answer 2.
Answer:
For shares of 'Asian Chemicals':
Let x = number of shares sold by Payal
Nominal value of each share = Rs 125
Face value of x shares = Rs 125x
Market value of each share = Rs 150
Market value of x shares = Rs 150x = proceeds from selling

Dividend = 12% of Rs 125x = \( \frac{12}{100} \times \) Rs 125x = Rs 15x ..........(i)

For shares of 'Saras Chemicals':
Market value of each share = Rs 40
Number of shares bought = \( \frac{\text{proceeds from selling 'Asian Chemicals'}}{\text{market value of 'Saras Chemicals'}} \) = \( \frac{150x}{40} \) = \( \frac{15x}{4} \)

Nominal value of each share = Rs 50
Face value of \( \frac{15x}{4} \) shares = Rs 50 × \( \frac{15x}{4} \) = Rs 187.5x

Dividend = 10% of Rs 187.5x = Rs \( \frac{10 \times 187.5x}{100} \) = Rs 18.75x .....(ii)

Step 1: Calculate increase in annual income.
Increase in annual income = Rs 825 = subtraction of (i) from (ii)
Rs (18.75x - 15x) = Rs 825
\( \Rightarrow \) 3.75x = Rs 825
\( \Rightarrow \) x = 220

Therefore, Payal sold 220 shares.
In simple words: Payal sold expensive Asian Chemical shares and bought cheaper Saras Chemical shares with the same money. She could buy more shares, so her dividend income increased by Rs 825 per year.

📝 Teacher's Note: Explain to students that when you sell expensive shares and buy cheaper ones with the same money, you get more shares. More shares usually means more dividend income.

🎯 Exam Tip: Calculate number of new shares carefully using the proceeds divided by new market price. Show all fraction calculations step by step.

Answer 3.
Answer:
For shares of 'Esco':
Let x = number of shares sold by Ananth
Nominal value of each share = Rs 50
Face value of x shares = Rs 50x
Market value of each share = Rs 80
Market value of x shares = Rs 80x = proceeds from selling

Dividend = 6% of Rs 50x = \( \frac{6}{100} \times \) Rs 50x = Rs 3x ..........(i)

For shares of 'Y2K Software':
Market value of each share = Rs 150
Number of shares bought = \( \frac{\text{proceeds from selling 'Esco'}}{\text{market value of 'Y2K Software'}} \) = \( \frac{80x}{150} \) = \( \frac{8x}{15} \)

Nominal value of each share = Rs 100
Face value of \( \frac{8x}{15} \) shares = Rs 100 × \( \frac{8x}{15} \) = Rs 53.33x

Dividend = 11% of Rs 53.33x = Rs \( \frac{11 \times 53.33x}{100} \) = Rs 5.86x .....(ii)

Step 1: Calculate increase in annual income.
Increase in annual income = Rs 2,150 = subtraction of (i) from (ii)
Rs (5.86x - 3x) = Rs 2,150
2.86x = Rs 2,150
\( \Rightarrow \) x = 751

Therefore, Ananth sold 751 shares.
In simple words: Ananth sold cheaper Esco shares and bought expensive Y2K Software shares. Even though he got fewer shares, each share gave more dividend, so his total income increased.

📝 Teacher's Note: Show students that sometimes buying fewer shares of a high-dividend company can give more income than many shares of a low-dividend company.

🎯 Exam Tip: When dealing with fractions like 8x/15, convert to decimal (53.33x) to make calculations easier. Always round final answer to nearest whole number of shares.

Answer 4.
Answer:
Given:
Total money to invest = Rs 10,000
Krithika wants 8% return on total investment

Step 1: Calculate income from 6% shares.
Amount invested in 6% shares = Rs 4,500
Market value = Rs 75
Income = Rs \( \frac{6}{75} \times 4,500 \) = Rs 360

Step 2: Calculate income from 8% shares.
Amount invested in 8% shares = Rs 2,500
Market value = Rs 100
Income = Rs \( \frac{8}{100} \times 2,500 \) = Rs 200

Step 3: Set up equation for 16% shares.
Let market value of 16% shares = Rs x
Amount invested in 16% shares = Rs (10,000 - 4,500 - 2,500) = Rs 3,000
Income from 16% shares = Rs \( \frac{16}{x} \times 3,000 \) = Rs \( \frac{48,000}{x} \)

Step 4: Calculate total required income.
Total required income = 8% of Rs 10,000 = Rs 800

Step 5: Set up final equation.
Rs 800 = Rs 360 + Rs 200 + Rs \( \frac{48,000}{x} \)
Rs 240x = Rs 48,000
x = Rs 200

Therefore, Krithika bought 16% shares at Rs 200 per share.
In simple words: Krithika wanted Rs 800 total income. She already got Rs 560 from two types of shares. The third type must give Rs 240 more. We calculated the price needed to get this income.

📝 Teacher's Note: Explain that dividend yield = (dividend rate/market price) × 100. Students should remember this formula. Higher market price means lower yield for same dividend rate.

🎯 Exam Tip: Always calculate total required income first (8% of Rs 10,000 = Rs 800). Then find how much more income is needed from the unknown shares. This method prevents calculation errors.

Answer 5.
Answer:
Money invested = Rs 35,000

For 'Lakme' shares:
Market value = Rs 40
Amount invested = Rs 6,000
Income from investment = \( \frac{6}{40} \times Rs 6,000 = Rs 900 \)

For 'Volta' shares:
Market value = Rs 125
Amount invested = Rs 15,000
Income from investment = \( \frac{8}{125} \times Rs 15,000 = Rs 960 \)

For 'BPL' shares:
Market value = Rs x
Amount invested = Rs (35,000 - 6,000 - 15,000) = Rs 14,000
Income from investment = Rs \( \frac{12}{x} \times 14,000 = Rs \frac{1,68,000}{x} \)

Total investment from shares = Rs 900 + Rs 960 + Rs \( \frac{1,68,000}{x} \)

Pramod wants \( 8\frac{1}{7} \)% return on his investment = \( \frac{57}{7} \)%

\( \frac{57}{100 \times 7} \times Rs 35,000 = Rs 2,850 \)

Therefore,
Rs 2,850 = Rs 900 + Rs 960 + Rs \( \frac{1,68,000}{x} \)
Rs 990x = Rs 1,68,000
x = Rs 169.69 = Rs 170

Hence, Pramod bought BPL shares at Rs 170 per share.
In simple words: Pramod invested money in three different company shares. He wanted a fixed return on his total investment. We calculated the return from two companies and then found what the third company's share price should be to give him the exact return he wanted.

📝 Teacher's Note: Help students understand that dividend rate and market price are different things. The dividend rate is given by the company, but you pay the market price to buy shares. Show them how to set up the equation step by step.

🎯 Exam Tip: Always write the total return equation clearly. Show all three parts of income separately. Round the final answer to the nearest rupee. Write "Hence" before your final answer to show conclusion.