Share and Dividend Class 10 ML Aggarwal Solutions for ICSE Maths Ch-3. Step by step solutions of Chapter 3 questions in simple and easy way to grasp the topics easily. Visit official Website CISCE  for detail information about ICSE Board Class-10 Mathematics.

Share and Dividend Class 10 ML Aggarwal Solutions for ICSE Maths

Board	ICSE
Class	10
Subject	Mathematics
Book	ML Aggarwal
Chapter-3	Share and Dividend
Topics	Solution of Exe-3 Questions
Edition	2025-2026

Share and Dividend

 Class 10 ML Aggarwal Solutions for ICSE Maths Ch-3

Que-1: Find the dividends received on 60 shares of Rs 20 each if 9% dividend is declared.

Sol:  FV of shares = Rs. 20

the value of 60 shares = Rs. 20 × 60

= Rs. 1200

rate of dividend = 9%

total dividend = Rs. 1200 × 9%

= 1200 × (9/100)

= Rs 108

Que-2: A company declares 8 per cent dividend to the shareholders. If a man receives Rs. 2840 as his dividend, find the nominal value of his shares.

Sol:    rate of dividend = 8%

amount of dividend = Rs. 2840

nominal value of shares = (2840 × 100)/8

= Rs. 35500

Que-3: 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 the dividend received by him in cash

Sol: FV of shares = Rs. 10

Number of shares = 200

Total  face value of 200 shares = 10 × 200

= Rs. 2000

Now, the amount invested for the purchase of 200 shares at the rate of Rs. 12.50 each

= 12.50 × 200

= Rs. 2500

rate of dividend = 8%

total amount of dividend = (2000 × 8)/100

= Rs. 160

Que-4: Find the market price of 5% Rs. 100 share when a person gets a dividend of Rs. 65 by investing Rs. 1430.

Sol:  amount of dividend = Rs. 65

rate of dividend = 5%

total face value = (65 × 100)/5

= Rs. 1300

If the face value is Rs. 1300, then the market value = Rs. 140

If the face value is Rs. 100, then the market value = (1430 × 100)/ 1300

= Rs. 110

Que-5: 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% p.a., 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?

Sol:  Given FV = Rs. 100

(i) Given MV = Rs. 132

And the number of shares = 50

So investment = number of shares × market value

= 50 × 132

= Rs. 6600

(ii)  income per share = 7.5% of the face value

= (75/ 10 × 100) × 100

= Rs. 7.5

So annual income = 7.5 × 50

= Rs. 375

(iii)  new annual income = 375 + 150 = Rs. 525

the number of shares = 525/7.5 = 70

number of extra shares to be increased = 70 – 50

= 20

Que-6: A lady holds 1800, Rs. 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return does she get on her investment? Give your answer to the nearest integer

Sol:  total number of shares = 1800

FV of each share = Rs. 100

And rate of dividend = 15%

Total face value of 1800 shares = 100 × 1800

= Rs. 180000

Hence, total dividend = 180000 × 15/100

= Rs. 2700

Hence market value of one share = 100 + 40 = Rs. 140

Now the total investment = 140 × 1800

= Rs. 252000

Hence, the percentage of his return

= (27000 × 100)/ 252000

= 10.7%

Que-7: What sum should a person invest in Rs. 25 shares, selling at Rs. 36, and obtain an income of Rs. 720, if the dividend declared is 12%? Also, find the percentage return on his income

Sol:  NV of each share = Rs. 25

MV of each share = Rs. 36

Total income = Rs. 720

and Rate of dividend = 12%

Therefore total nominal value = (100 × 720)/ 12

= Rs. 6000

Number of shares = 6000/25

= 240

Hence Total investment = 240 × 36

= Rs. 8640 ( Ans of first part )

Now, percentage return = (720 × 100)/ 8640

= 8.3%  ( Ans of second part )

Que-8: Ashok invests Rs. 26400 on 12% Rs. 25 shares of a company. If he receives a dividend of Rs. 2475, find:

(i) The number of shares he bought.

(ii) The market value of each share.

Sol:   investment = Rs. 26400

Face value of each share = Rs. 25

Rate of dividend = 12%

and Total dividend = Rs. 2475

Annual dividend  = NV of a share × number of shares × r/100

(i) Therefore number of shares = (2475/12) × (100/25)

= 825 shares

(ii) Market value of each share = (26400/825)

= Rs. 32

Que-9: A man invests ₹ 4500 in shares of a company which is paying 7.5% dividend. If ₹ 100 shares are available at a discount of 10%, find

(i) the number of shares he purchases.

(ii) his annual income.

Sol:  Investment = ₹ 4500

Face value of each share = ₹ 100

Discount = 10%

and rate of dividend = 7.5%

The MV of each share = ₹ (100 – 25) = ₹ 75

(i) The number of shares he purchases = 4500/75 = 60

(ii) Dividend = ₹ 7.5% of (60 x 100)

= ₹ 450

Hence, his annual income will be ₹ 450.

Que-10:  Amit Kumar invests Rs. 36000 in buying Rs. 100 shares at Rs. 20 premium. The dividend is 15% per annum. Find:

(i) The number of shares he buys
(ii) His yearly dividend
(iii) The percentage return on his investment.

Sol:   investment = Rs. 36000

Face value = Rs. 100

Premium = Rs. 20

and dividend = 15%

(i) Number of shares = 36000/120

= 300

(ii) Dividend = 15% 0f (100 × 300)

= Rs. 4500

(iii) Percentage of return = (4500/36000) × 100

= 450/36

= 12.5%

Que-11:  Mr. Tiwari invested Rs. 29040 in 15% Rs. 100 shares at a premium of 20%. Calculate:

(i) The number of shares bought by Mr. Tiwari

(ii) Mr. Tiwari’s income from the investment

(iii) The percentage return on hid investment.

Sol:  (i) Market value of one share = [(200/100) × 100] + 100

= Rs. 120

Number of shares = investment/ market value of one share

= 29040/120

= Rs 242

(ii) Therefore, the income from investment = 242 × 15

= Rs 3630

(iii) Percentage return on his investment = (dividend/ market value) × 100

= (15/120) × 100

= 12.5%

Que-12: A man buys shares at the par value of Rs. 10, yielding 8% dividend at the end of a year. Find the number of shares bought if he receives a dividend of Rs. 300.

Sol:   FV of each share = Rs. 10

Rate of dividend = 8% per annum

and Total dividend = Rs. 300

Therefore total face value of shares = (300 × 100)/ 8

= Rs. 3750

Number of shares = 3750/10

= 375

Que-13: A man invests Rs. 8800 on buying shares of the face value of rupees hundred each at a premium of 10%. If he earns Rs. 1200 at the end of the year as a dividend, find:

(i) The number of shares he has in this company

(ii) The dividend percentage per share.

Sol:   investment = Rs. 8800

FV of each share = Rs. 100

MV of each share = 100 + 10 = Rs. 110

Total income = Rs. 1200

Hence total Nominal value = (8800 × 100)/ 110

= Rs. 8000

(i) Number of shares = 8000/100

= 80

(ii) Rate of dividend = (1200 × 100)/ 8000

= 15%

Que-14: 14. A man invested Rs. 45000 in 15% Rs. 100 shares quoted at Rs. 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 shares.

Sol: Total investment  = Rs. 45000

FV of each share = Rs. 125

Hence total number of shares = 45000/125

= 360 shares

Income from sold shares = Rs. 8400

Therefore, the number of shares sold = income from shares/ number of shares sold

= 8400/ 140

= 60

(i) Number of shares he still holds = 300

(ii) Market value of 300 shares = 300 × 140

= Rs. 42000

Face value of 300 shares = 300 × 125

= Rs. 37500

Difference = Market value – face value

= 42000 – 37500

= Rs. 4500

Que-15: Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend 0f 9%. Calculate

(i) The dividend that Ajay will get
(ii) The rate of interest on his investment if Ajay has paid Rs. 30 for each share.

Sol:   number of shares = 560

Face value  = Rs. 25

and Rate of dividend = 9%

Total face value of 560 shares = 25 × 560

= Rs. 14000

(i) Amount of dividend = 14000 × (9/100)

= Rs. 1260

(ii) MV of each share = Rs. 30

So Total investment = 30 × 560

= Rs. 16800

Hence percentage of interest on his investment

= (1200 × 100)/ 16800

= 7.5%

Que-16:  A company with 10000 shares of nominal value of Rs. 100 declares an annual dividend of 8% to the shareholders.

(i) Calculate the total amount of dividend paid by the company
(ii) Ramesh bought 90 shares of the company at Rs. 150 per share. Calculate the dividend he received and the percentage return on his investment.

Sol:  (i) number of shares = 10000

FV of each share = Rs. 100

and Rate of annual dividend = 8%

Total face value  = 100 × 10000

= Rs. 1000000

Dividend = (1000000 × 8)/ 100

= Rs. 80000

(ii) Number of shares = 90

FV of each share = Rs. 150

FV of 90 shares = 100 × 90

= Rs. 9000

Hence amount of dividend = (9000 × 8)/ 100

= Rs 720

Market value of 90 shares = 90 × 159

= Rs 13500

Hence, the rate of interest = (720 × 100)/ (13500 × 1)

= 16/3

= 5.3 %

Que-17:  A company with 4000 shares of nominal value of Rs. 110 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. (2008)

Sol:  Number of shares = 4000

Nominal (face) value of each share = Rs. 110

Total face value of 4000 shares = Rs. 110
x 4000

= Rs. 440000

Rate of annual dividend = 15%

(i) Amount of dividend = (440000 x 15)/ 100

= Rs. 66000

(ii) Number of shares Shah Rukh has = 88

Face value of 88 shares = 88 x 110

= Rs. 9680

Annual dividend = (9680 x 15)/ 100

= Rs. 1452

(iii) Rate of annual income on his investment = 10%

His investment = (1452 x 100)/ 10

= Rs. 14520

Market value of each share = 14520/88

= Rs. 165

Que-18: By investing Rs. 7500 in a company paying 10 per cent dividend, an income of Rs. 500 is received. What price is paid for each Rs. 100 share?

Sol:   investment = Rs. 7500

Rate of dividend = 10%,

Total income = Rs. 500.

and Face value of each share = Rs. 100

Total face value = (100 x 500)/10

= Rs. 5000

If the face value is Rs. 5000, then investment = Rs. 7500

And if the face value is Rs. 100, then the market value of each share = (7500 x 100)/ 5000

= Rs 150

Que-19: A man buys 400 ten-rupee shares at a premium of Rs. 2.50 on each share. If the rate of dividend is 8%, Find,

(i) his investment

(ii) dividend received

(iii) yield.

Sol:  Total shares = 400

FV of each share = Rs. 10

The MV of each share

= Rs. 10 + Rs. 2.50

= Rs. 12.50

Rate of dividend = 8%

Hence, the face value of 400 shares = 10 x 400

= Rs. 4000

(i) Total investment = 12.50 x 400

= Rs. 5000

(ii) Total dividend = 4000 x (8/100)

= Rs. 320

(iii) Yield percent = (320 x 100)/ 5000

= 32/5

= 6.4%

Que-20: A man invests Rs. 10400 in 6% shares at Rs. 104 and Rs. 11440 in 10.4% shares at Rs. 143. How much income would he get in all?

Sol:   In first case

Total investment = Rs. 10400

Rate of dividend = 6%

Market value of each share = Rs. 104

Total dividend = (10400 x 6)/ 104

= Rs. 600

 in second case  

investment = Rs. 11440

Rate of dividend = 10.4%

The market value of each share = Rs. 143

Therefore, total dividend = (11440 x 10.4)/ 143

= Rs. 832

Total dividend from both cases = Rs. 600 + Rs. 832

= Rs. 1432

Que-21: Two companies have shares of 7% at Rs. 116 and 9% at Rs. 145, respectively. In which of the shares would the investment be more profitable?

Sol:  Let the investment in each case = Rs. 116 x 145

Dividend in the first case,

= (116 x 145 x 7)/ 116

= Rs. 1015

Dividend in the second case

= (116 x 145 x 9)/ 145

= Rs. 1044

the second type of shares is more profitable

Que-22: Which is the better investment: 6% Rs. 100 shares at Rs. 120 or 8% Rs. 10 shares at Rs. 15?

Sol: Let the investment in each case = Rs. 120 In the first case,

Dividend on Rs. 120 = Rs. 6

In the second case, a dividend on Rs. 10

= (8 x 10)/ 100

= 0.8

Now dividend on Rs. 15 = 0.8

Then dividend on Rs. 120 = (0.8 x 120)/ 15

= Rs. 6.4

Hence  the second type of shares, is more profitable.

Que-23:  A man invests Rs. 10080 in 6% hundred- rupee shares at Rs. 112. Find his annual income. When the shares fall to Rs. 96, he sells out the shares and invests the proceeds in 10% ten-rupee shares at Rs. 8. Find the change in his annual income.

Sol:   Investment = Rs. 10080

Face value of each share = Rs. 100

Market value of each share = Rs. 112

and Rate of dividend = 6%

Total income for the year

= (10080 x 6)/ 112

= Rs. 540

Number of shares = 10080/112

= 90

Selling price of 90 shares at the rate of Rs. 96 each = 90 x 96

= Rs. 8640

Rate of dividend in new shares = 10%

Face value of each share = Rs. 10

The market value of each share = Rs. 8

Number of shares = 8640/8 = 1080

Face value of 1080 shares = 1080 x 10

= Rs. 10800

Dividend = (10800 x 10)/100

= Rs. 1080

Difference in income = 1080 – 540

= Rs. 540 more

Que-24: Sachin invests ₹ 8500 in 10% ₹ 100 shares at ₹ 170. He sells the shares when the price of each share rises by ₹ 30. He invests the proceeds in 12% ₹ 100 shares at ₹ 125. Find

(i) the sale proceeds.

(ii) the number of ₹ 125 shares he buys.

(iii) the change in his annual income.

Sol:  Investment = ₹ 8500

Face value of each share = ₹ 100

The market value of each share = ₹ 170

Rate of dividend = 10%

Total income for the year

= ₹ (8500 x 10)/170

= ₹ 500

And, the number of shares = 8500/170 = 50

Selling price of 50 shares at the rate of ₹ (170 + 30) each = ₹ 50 x 200

= ₹ 10000

(i) The sale proceeds = ₹ 10000

Rate of dividend in new shares = 12%

Face value of each share = Rs. 100

The market value of each share = Rs. 125

(ii) Number of shares = 10000/125 = 80

Face value of 80 shares = ₹ 80 x 100

= ₹ 8000

Dividend = ₹ (8000 x 12)/100

= ₹ 960

(iii) Hence, the change in his annual income = ₹ (960 – 500)

= ₹ 460 more

Que-25:  A person invests Rs. 4368 and buys certain hundred-rupee shares at 91. He sells out shares worth Rs. 2400 when they have t risen to 95 and the remainder when they have fallen to 85. Find the gain or loss on the total transaction.

Sol:   Investment = Rs. 4368

Market value of each share = Rs. 91

Face value of each share = Rs. 100

So, number of shares = 4368/91

= 48

FV of 24 shares = 24 x 100

= Rs. 2400

Sale price of shares worth Rs. 2400 = (2400 x 95)/ 100

= Rs. 2280

Face value of remaining shares = 24 x 100

= Rs. 2400

Sale price of shares of remaining amount = (2400 x 85)/ 100

= Rs. 2040

Total amount received = 2280 + 2040

= Rs. 4320

Loss = 4368 – 4320

= Rs. 48

Que-26: By purchasing Rs. 50 gas shares for Rs. 80 each, a man gets 4% profit on his investment. What rate per cent is the company paying? What is his dividend if he buys 200 shares?

Sol:   market value  = Rs. 80

Face value  = Rs. 50

Interest on investment = 4%

Dividend on Rs. 80 = (80 x 4)/ 100

= 32/10

Percent dividend = (32/10) x (100/50)

= 64/10

= 6.4%

Number of shares = 200

Face value of 200 shares = 200 x 50

= Rs. 10000

Dividend = Rs. 10000 x (6.4/100)

= Rs. 640

Que-27: Rs. 100 shares of a company are sold at a discount of Rs. 20. If the return on the investment is 15%. Find the rate of dividend declared.

Sol:  Market value of each shares

= 100 – 20 = Rs.80

Interest on investment of Rs. 80 = 15% x 80

= 80 x 15/100

= Rs. 12

Dividend on the face value of Rs. 100 = Rs. 12

Rate of dividend = 12%.

Que-28:  A company declared a dividend of 14%. Find the tire market value of Rs. 50 shares if the return on the investment was 10%.

Sol: Rate of dividend = 14%

Dividend on Rs. 50 = (14 x 50)/ 100

= Rs. 7

Now Rs. 10 is interest on the investment of = Rs. 100

Rs. 7 will be the interest on = (100 x 7)/ 10 = Rs. 70

Hence, the market value of Rs. 50 shares = Rs. 70

Que-29:   A company with 10000 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% on his investment, find the price he paid for each share.

Sol:  , No. of shares = 10000

Face value of each share = Rs. 100

Rate of dividend = 5%

(i) Total face value of 10000 shares

= Rs. 100 x 10000

= Rs. 1000000

Total amount of dividend = Rs. (1000000 × 5)/100

= Rs. 50000

(ii) Income of 72 shares = 72 × 5 = Rs. 360

(iii) Rate of interest on investment = 4%

Hence, market value of each share = Rs. 100/4 × 5

= Rs. 125

Que-30: A man sold some Rs. 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in Rs. 100 shares paying 16% dividend quoted at Rs. 80 and thus increased his income by Rs. 2000. Find the number of shares sold by him

Sol:   Face value of each share = Rs. 100

The market value of each share = Rs. 100 – Rs.25

= Rs. 75

Rate of dividend = 10%

Let the no. of shares be taken as x

Selling price = x × 75 = Rs. 75x

Face value of x shares = 100 x

Dividend annually = 100x × 10/100 = 10x

No. of shares purchased = 75x/80 = 15x/16

Face value of 15x/16 shares = 15x/16 × 100 = 1500x/16

Now, dividend = 1500x/16 × 16/100 = 15x

Thus, the increase in the income = 15x – 10x = 5x

5x = 2000

x = 2000/5 = 400

Hence, the number of shares purchased = 400

Que-31: A man invests Rs. 6750, partly in shares of 6% at Rs. 140 and partly in shares of 5% at Rs. 125. If his total income is Rs. 280, how much has he invested in each?

Sol:  Let’s  investment in  first case = x

Then, the investment in second case = (6750 – x)

In first case, the dividend = Rs. x × (6/140)

= Rs. 3x/70

while dividend in second case = Rs. (6750 – x) × (5/125) = Rs. (6750 – x)/25

Total dividend = 3x/70 + (6750 – x)/25

But the total income given = Rs. 280

so equalize both

3x/70 + (6750 – x)/25 = 280

15x + 14(6750 – x) = 280 × 350 [Since, L.C.M = 350]

x = Rs. [(280 × 350) – (14 × 6750)]

= Rs. (98000 – 94500)

= Rs. 3500

Hence, investment in the first case = Rs. 3500

And investment in the second case = Rs. 6750 – Rs. 3500

= Rs. 3250

Que-32: Divide Rs. 20304 into two parts such that if one part is invested in 9% Rs. 50 shares at 8% premium, and the other part is invested in 8% Rs. 25 shares at 8% discount, then the annual incomes from both the investment are equal.

Sol:   Total amount = Rs 20304

Let the amount invested in 9% Rs 50 at 8% premium = x

Then, the amount invested in 8% Rs 25 at 8% discount = 20304 – x

given that Income from both investments is equal

Now, income from the first type

= (x × 9)/(100 + 8)

= 9x/108

= x/12

Income from the second type

= [(20304 – x) × 8]/(100 – 8)

= [(20304 – x) × 8]/92

= 2(20304 – x)/23

both cases the annual income

So   x/12 = 2(20304 – x)/23

23x = 24(20304 – x) [After cross multiplication]

23x = 24 × 20304 – 24x

23x + 24x = 24 × 20304

47x = 24 × 20304

x = (24 × 20304)/47

= 10368

Hence, the amount invested in first type = Rs. 10368

And amount in the second type

= Rs. 20304 – Rs. 10368

= Rs. 9936

— : End of Share and Dividend Class 10 ML Aggarwal Solutions for ICSE Maths Ch-3 questions :–

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