# ML Aggarwal Solutions for Chapter 3 Shares and Dividends Class 10 Maths ICSE

Here, we are providing the solutions for Chapter 3 Shares and Dividends from ML Aggarwal Textbook for Class 10 ICSE Mathematics. Solutions of the third chapter has been provided in detail. This will help the students in understanding the chapter more clearly. Class 10 Chapter 3 Shares and Dividends ML Aggarwal Solutions for ICSE is one of the most important for the board exams which is based on the share market, face value and profit.

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

Value of one share = Rs 20

Value of 60 shares = Rs 20 × 60

= Rs 1200

Rate of Dividend = 9%

∴ Total dividend = Rs 1200 × 9%

= Rs 1200 × 9/100 = Rs 108

2. A company declares 8 percent dividend to the share holders. If a man receives Rs 2840 as his dividend, find the nominal value of his shares.

Rate of dividend = Rs 2840

∴ Nominal value of shares = (2840 × 100)/8

= Rs 35500

3. A many 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.

Face value of 200 shares = Rs 10 × 200 = Rs 2000

(i) Amount invested for the purchase of 200 shares at the rate of Rs 12.50 each

= Rs 12.50 × 200 = Rs. 2500

(ii) Rate of dividend = 8%

∴ Total amount of dividend = Rs (2000 × 8)/100 = Rs 160

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

Amount of dividend = Rs 65

Rate of dividend = 5%

∴ Total face value = (65 × 100)/5 = Rs 1300

If face value is Rs. 1300, then market value = Rs. 1430

And if face value is Rs. 100, then market value = (1430 × 100)/1300 = Rs 110

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 be

Face value = Rs 100

(i) Market vale = Rs 132

No. of Shares = 50

Investment = no. of shares × Market value

= 50 × 132 = Rs 6600

(ii) Income per share = 7.5% of Face value

= 75/(10 × 100) × 100 = ₹ 7.5

∴ Annual incomes = 7.5 × 50 = ₹ 375

(iii) New annual income = 375 + 150

= ₹ 525

∴ No. of shares = 525/7.5 = 70

∴ No. of extra share to be increased = 70 – 50 = 20

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.

Total number of shares = 1800

Nominal value of each share = Rs 100

Rate of dividend = 15%

(i) Total face value of 1800 shares = Rs 100 × 1800

= Rs 18000

∴ Total dividend = Rs 180000 × 15/100

= Rs 27000

(ii) Market value of each share = Rs 100 + Rs 40 = Rs 140

∴ Total investment = Rs 140 × 1800

= Rs 252000

∴ Percentage on his return = (27000 × 100)/252000

= 10.7 = 11% (in integers)

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

(i) The number of shares bought by him.

(ii) The percentage return on his income.

Nominal value of each share = Rs 25

Market value of each share = Rs 36

Total income = ₹ 720

Rate of dividend = 12%

Total nominal value = 100/12 × 720

= ₹ 6000

(i) ∴ Numbers of shares = 6000/25 = 240

Total investment = 240 × ₹ 36 = ₹ 8640

(ii) Percentage return = (720 × 100)/8640 = 8.33 %

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.

Given investment = Rs 26400

Face value of the each share = Rs 25

Rate of dividend = 12%

Total dividend = Rs 2475

We know that, dividend earned = market price of 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

9. Amit Kumar Rs 36,000 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.

Investment = Rs 36000

Face value = Rs 100

Premium = Rs 20, dividend = 15%

(i) No. of shares = 36000/120 = 300

(ii) Dividend = 15% of (100 × 300) = ₹ 4500

(iii) Return = 4500/3600 × 100 = 450/36 = 12.5% = 13%

10. Mr. Tiwari invested Rs 29040 in 5% 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 his investment.

(i) M.V. of one share = [20/100 × 100 + 100]

= Rs 120.

No. of shares = Investment/(M.V. of 1 share)

= ₹ 29040/120

= ₹ 242

(ii) Income = 242 × 15

= ₹ 3630

(iii) rate % = dividend/M.V. × 100

= 15/120 × 100

= 12.5%

11. 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.

Face value of each share = Rs 10

Rate of dividend = 8% p.a.

Total dividend = Rs 300

∴ Total face value of shares = (300 × 100)/8 = ₹ 3750

And no. of shares = ₹ 3750/10 = 375

12. A man invests Rs 8000 on buying of face value of rupees hundred each at a premium of 10%. If he earns RS 1200 at the end of year as dividend, find:

(i) the number of shares he has in the company.

(ii) the dividend percentage per share.

Investment = Rs 8800

Face value of each share = Rs 100

And market value of each share = Rs 100 + Rs 10

= Rs 110

Total income = Rs 1200

Total face value = Rs (8800 × 100)/100

= Rs 8000

(i) No. of shares = 8000/100

= 80

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

= 15%

13. 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.

Investment on shares = Rs 45000

Face value of each share = Rs 125

∴ Total number of shares = 45000/125 = 360 shares

Income from sold shares = Rs 8400

No. of shares sold

= (Income from shares)/(Market value of each share)

= 8400/140 = 60

∴ 60 shares were sold.

(i) No. of shares he still hold = Total number od shares – sold shares

= 360 – 60

= 300 shares.

∴ Number of shares he still holds = 300

(iii) Market value of 300 shares = Rs 300 × 125

= Rs 37500

Face value of 300 shares = Rs 300 × 125 = Rs 37500

Difference = Market value – Face value

= Rs 42000 – Rs 37500

= Rs 4500

14. A company pays a dividend of 15% on its ten-rupee shares from which it deducts tax at the rate of 22%. Find the annual income of a man, who owns thousand shares of this company.

No. of shares = 1000

Face value of each are = Rs 10

Rate of dividend = 15%,

Rate of tax deducted = 22%

Total face value of 1000 shares = Rs 10 × 1000

= Rs 10000

Total dividend = Rs 10000 × 15/100

= Rs 1500

Tax deducted at the rate of 22% = Rs 1500 × 22/100 = Rs 330

Net annual income = Rs 1500 – Rs 330 = Rs 1170

15. 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 has paid Rs 30 for each share.

No, of shares = 560

Face value of each share = Rs 25

Rate of dividend = 8% p.a.

Total face value of 560 shares = Rs 25 × 560

= Rs 14000

16. A company with 10000 shares of nominal value of Rs 100 declares an annual dividend of 8% to the share holders.

(i) Calculate the total amount of dividend paid by the company.

(ii) Ramesh bought90 shares of the company at Rs.150 per share.

Calculate the dividend he received and the percentage return on his investment.

(i) Number of shares = 10000

Nominal value of each share = Rs 100

Rate of annual dividend = 8%

Total face value of 10000 shares = Rs 100 × 10000

= Rs 1000000

And amount dividend = Rs (1000000 × 8)/100

= Rs 80000

(ii) Number of shares = 90

Face value of each share = Rs 150

Total face value of 90 shades = 100 × 90

= Rs 9000

∴ Amount of dividend = Rs (9000 × 8)/100

= Rs 720

Marked value of 90 shares = 90 × 150

= Rs 13500

∴ Rate of interest = (720 × 100)/(13500 × 1)

= 16/3 = 5.33%

17. A company with 4000 shares of nominal value of Rs 110 declares 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.

Number of shares = 4000

Nominal (face) value of each share = Rs 110

Total face value of 4000 shares = Rs 110 × 4000

= Rs 440000

Rate of annual dividend = 15%

(i) Amount of dividend = (44000 × 15)/100 = Rs 66000

(ii) Number of shares, Shah Rukh has = 88

∴ Face value of 88 shares = 88 × 110 = Rs 9680

And annual dividend = Rs (9680 ×15)/100 = Rs 1452

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

∴ His investment = (1452 × 100)/10 = Rs 14520

And Market value of each share = 14520/88 = Rs 165

18. By investing Rs 7500 in a company paying 10 percent dividend, an income of Rs 500 is received. What price is paid for each Rs 100 share

Investment = Rs 7500

Rate of dividend = 10%,

Total income = Rs 500

Face value of each share = Rs 100

Total face vale = (100 × 500)/10 = Rs 5000

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

And if face value is Rs 100 then market value of each share = (7500 × 100)/5000

= Rs 150

19. A man invests Rs 8000 in a company paying 8% dividend when a share of face value of Rs 100 is selling at Rs. 60 premium,

(i) What is his annual income,

(ii) What percent does he get on his money?

Investment = Rs 8000

Face value of each share = Rs 100

Market value = Rs 100 + Rs 60 = Rs 160

Rate of dividend = 8% p.a.

(i) Annual income = (8 × 8000)/160 = Rs 400

(ii) Rate of interest on his money = (400 × 100)/8000 = 5%

20. A man buys 400 ten-rupee shares at a premium of Rs. 2.50 on each share. If the rate of dividend ids 8%, find,

(i) his investment

(ii) yield

No of shares = 400

Face value pf each share = Rs 0

Market value of each share = Rs 10 + Rs 2.50 = Rs 12.50

Rate of dividend = 8%

∴ Face value of 400 shares = Rs 10 × 40

= Rs 4000

(i) Total investment = Rs 12.50 × 400 = Rs 5000

(ii) Total dividend = Rs 4000 × 8/100 = Rs 320

(iii) Yield percent = (320 × 100)/5000 = 32/5 = 6.4%

21. A man invests Rs. 10400 in 6% shares at Rs 104 an Rs 11440 in 10.4% shares at Rs 143. How much income would he get in all?

In first case; Total investment = Rs 10400

Rate of dividend = 6%

Market value of each share = Rs 104

∴ Total dividend = (10400 × 6)/104

= Rs 600

In second case,

Investment = Rs 11440

Rate of dividend = 10.4%

Market value of each share = Rs 143

∴ Total dividend = Rs (11440 × 10.4)/143

= Rs 832

Total dividend from both cases = Rs 600 + Rs 832

= Rs 1432

22. 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?

Let the investment in each case = Rs 116 × 145

Dividend in first case

∴ Dividend in first case = Rs. (116 × 145 × 7)/116 = Rs 1015

23. Which is better investment : 6% Rs 100 shares at Rs 120 or 8% Rs 10 shares at Rs 15

Let the investment in each case = Rs 120

In the first case,

Dividend on Rs 120 = Rs 6

In second case, dividend on Rs 10

= (8 × 10)/100 = 0.8

Now dividend on Rs 15 = 0.8

Then dividend on Rs 120 = (0.8 × 120)/15 = Rs 6.4

It is clear that, second investment i.e. 8%

Rs 10 shares at 15 is more profitable.

24. 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.

Investment = Rs 10080

Face value of each share = Rs 100

Market value of each share = Rs 112

Rate of dividend = 6%

Total income for the year = (10080 × 6)/112 = Rs 540

No. of shares = 10080/112 = 90

Selling price of 90 shares at the rate of Rs 96 each = 90 × 96 = Rs 8640

Rate of dividend in new shares = 10%

Face value of each share = Rs 10

And market value of each share = Rs 8

No. of shares = 8640/8 = 1080

Face value of 1080 shares = 1080 × 10

= Rs 10800

∴ Dividend = Rs (10800 × 10)/100 = Rs 1080

Difference in income = Rs 1080 – Rs 540 = Rs 540 more

25. A man bought 369 ten-rupee shares paying 12% per annum. He sold them when the price rose to Rs 21 and invested the proceeds in five-rupee shares paying 4.1/2 per annum at Rs 3.5 per share. Find the annual charge in his income.

No. of shares bought = 360

Face value of each share = Rs 10

Rate of dividend = 12%

Total face value of 360 shares = Rs 10 × 360

= Rs 3600

Yearly dividend = Rs (3600 × 12)/100 = Rs 432

On selling the share at Rs 21, the amount received = Rs 21 × 360

= Rs 7560

Face value of new shares = Rs 5.00

And market value = Rs 3.5

Rate of dividend = 4.1/2% = 9/2%

No. of shares purchased = 7560/3.5

= (7560 × 10)/35 = 2160

Face value of 2160 shares = Rs 5 × 2160

= Rs 10800

Dividend = (10800 × 9)/(100 × 2) = Rs 486

Change in income = Rs 486 – Rs 432 = Rs 54 gain

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

Investment = Rs 4368

Market value of each share = Rs 91

Face value of each share = Rs 100

No. of shares = 4368/91 = 48

Face value of 24 shares = 24 × 100 = Rs 2400

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

= Rs 2280

Face value of remaining shares = 24 × 100 = Rs 2400

Sale price of shares of remaining amount = (2400 × 85)/100 = Rs 2040

Total amount received = Rs 2280 + Rs 2040 = Rs 4320

Loss = Rs 4368 – Rs 4320 = Rs 48

27. By purchasing Rs 50 gas shares for Rs 80 each, a man gets 4% profit on his investment. What rate percent is company paying ? What is his dividend if he buys 200 shares ?

Market value of each share = Rs 80

Face value of each share = Rs 50

Interest on investment = 4%

Dividend on Rs 80 = (80 × 4)/100

= 32/100

Now dividend on face value Rs. 50 = 32/10

∴ Percent dividend = 32/10 × 100/50

= 64/10 = 6.4%

No. of shares purchased = 200

∴ Face value of 200 shares = Rs 200 × 50

= Rs 10000

Dividend = Rs 10000 × 6.4/100 = Rs 640

28. 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.

Market value of each shares = 100 – 20

= Rs 80

Interest on investment of Rs 80 = 15% × 80

= 15/100 × 80 = Rs 12

Dividend on face value of Rs 100 = Rs 12

Rate of dividend = 12%

29. A company declared a dividend of 14%. Find the market value of Rs 50 shares if the return on his investment was 10%.

Rate of dividend = 14%

Dividend on Rs 50 = (14 × 50)/100 = Rs 7

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

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

Hence market value of Rs 50 shares = Rs 70

30. At what price should a 6.25% Rs 100 shares be quoted when the money is worth 5%?

Interest on Rs 100 worth = Rs 5

If interest is Rs 5, then market value = Rs 100

And if interest id Rs 6.25, then market value = 100/5 × 6.25

= (100 × 6.25)/(5 × 100) = 125

Market value of each share = Rs 125

31. At what price should a 6.25% Rs 50 share be quoted when the money is worth 10%?

Interest on Rs 100

Worth = Rs 10

If the interest is Rs 10, then market value = Rs 100

And if interest is Rs 6.25, then market value = (50 × 6.25)/10

= (50 × 625)/(10 × 100)

= Rs 31.25

32.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.

No. of shares = 10000

Face value of each share = Rs 100

Rate of dividend = 5%

(i) Total face value of 10000 shares = Rs 100 × 10000

= Rs 1000000

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

= Rs 50000

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

(iii) Rate of interest on investment = 4%

∴ Market value of each share = 100/4 × 5

= Rs 125

33. A man sold some Rs 100 shares paying 10% dividend at a discount of 25% and investment 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.

Face value of each share = Rs 100

Market value of each share = Rs 100 – Rs 25 = Rs 75

Rate of dividend = 10%

Let no. of shares = x

Selling price = x × 75 = Rs 75x

Face value of x share = 100x

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

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

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

Dividend = 1500/16.x × 16/100 = 15x

∴ Increase in income = 15x – 10x = 5x

Now 5x = 2000

∴ x = 2000/5 = 400

∴ No. of shares purchased = 400

34. By selling at Rs 77, some 2.1/4% shares of face value Rs 100, and investing the proceeds in 6% shares of face value Rs 100, selling at 110, a person increased his income by Rs 117 per annum. How many shares did he sell?

Let the number of shares = x

On selling at Rs 77, the amount received x × 77 = Rs 77x

And dividend received = 77x × 9/(4 × 77) = 9/4x

Again investing Rs 77x for the purchase of shares of market value Rs 110 = 77x/110 shares

Dividend = 77x/110 ×6 = 42/10.x

Difference in income = 42/10.x – 9/4x

= (84x – 45x)/20

= 39/20.x

∴ 39/20x = 117

⇒ x = (117 × 20)/39

= 60

Hence, No. of shares sold = 60

35. 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?

Let’s consider the investment in first case to be x

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

= Rs 3x/70

And dividend in second case = Rs (6750 – x) × (5/125)

= Rs (6750 – x)/25

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

Given that the total income = Rs 280

So, we have

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 first case = Rs 3500

And investment in second case = Rs 6750 – Rs 3500

= Rs 3250

36. Divide Rs 20304 into two parts such that if one part is 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.

Given,

Total amount = Rs 20304

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

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

Income from both investments are equal now income from first type of shares

= (x ×9)/(100 + 8)

= 9x/108

= x/12

Income from the second type of shares = [{20304 – x) ×8]/(100 – 8)

= [(20304 – x) ×8)]/92

= 2(20304 – x)/23

As given, in both the cases the annual income is same, we have

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 kind of shares = Rs 10368

And in second kind of shares = Rs 20304 – Rs 10368

= Rs 9936

Multiple Choice Questions

1. If Jagbeer invest ₹ 10320 on ₹ 100 shares at a discount of ₹ 14, then the number of shares he buys is

(a) 110

(b) 120

(c) 130

(d) 150

(b) 120

Investment = ₹ 10320

Face value of each share = ₹ 100

M.V. of each share = ₹ 100 – 14 = ₹ 86

No. of shares = 10320/86 = 120

2. If Nisha invests ₹ 19200 on ₹ 50 shares at a premium of 20%, then the number of shares she buys is

(a) 640

(b) 384

(c) 320

(d) 160

(c) 320

Investment = ₹ 19200

Face value of each share = ₹ 50

M.V. = ₹ 50 × 120/100 = ₹ 60

Number of shares = 19200/60 = 320

3. ₹ 40 shares of a company are selling at 25% premium. If Mr. Jacob wants to buy 280 shares of the company, then the investment required by him is

(a) ₹ 11200

(b) ₹ 14000

(c) ₹ 16800

(d) ₹ 8400

(b) ₹ 14000

Face value of each share = ₹ 40

M.V. = 40 × 125/100 = ₹ 50

Number of shares = 280

Total investment = ₹ 280 × 50 = ₹ 14000

4. Arun possesses 600 shares of ₹ 25 of a company. If the company announces a dividend of 8%, then Arun’s annual income is

(a) ₹ 48

(b) ₹ 480

(c) ₹ 600

(d) ₹ 1200

(d) ₹ 1200

Number of shares = 600

F.V. of each share = ₹ 25

Rate of dividend = 8%

Annual income = 600 × 25 × 8/100 = ₹ 1200

5. A man invests ₹ 24000 on ₹ 60 shares at a discount of 20%. If the dividend declared by the company is 10%, then his annual income is

(a) ₹ 3000

(b) ₹ 2880

(c) ₹ 1500

(d) ₹ 1440

(a) ₹ 3000

Investment = ₹ 24000

F.V. of each share = ₹ 60

M.V. at discount of 20% = 60 × 80/100 = ₹ 48

Rate of dividend = 10%

∴ Face value of all share = (500 × 60)/48 = ₹ 30000

Annual dividend = ₹ (30000 × 10)/100 = ₹ 3000

6. Salman has some shares of ₹ 50 of a company paying 15% dividend. If his annual income is ₹ 3000, then the number of shares he possesses is

(a) 80

(b) 400

(c) 600

(d) 800

(b) 400

F.V. of each share = ₹ 50

Dividend = 15%

Annual income = ₹ 3000

Let x be the share, then

F.V. of shares = x × 50 = ₹ 50x

⇒ x = 400
∴ Number of shares = 400

7. ₹ 25 shares of a company are selling at ₹ 20. If the company is paying a dividend of 12%, then the rate of return is

(a) 10%

(b) 12%

(c) 15%

(d) 18%

(c) 15%

F.V. of each share = ₹ 25

M.V. = ₹ 20

Rate of dividend = 12%

Dividend on each share = 12/100 × 25 = ₹ 3

Return on ₹ 20 = ₹ 3

And on ₹ 100 = ₹ 3/20 × 5/100 = 15%

Chapter Test

1. If a man received ₹ 1080 as dividend from 9% ₹ 20 shares, find the number of shares purchased by him.

Income on one share = 9/100 × 20

= Rs 9/5

∴ No. of shares = 1080 × 5/9

= 120 × 5 = 600

2. Find the percentage interest on capital invested in 18% shares when a Rs 10 share costs Rs 12.

Dividend on one share = 18% of Rs 10

= (18 × 10)/100 = Rs 9/5

Income on ₹ 12 = 9/5

Then income of ₹ 100 = 9/5 × 100/12 = 15

∴ Percentage interest on capital = 15%

3. Rohit Kulkarni invests Rs 10000 in 10% Rs 100 shares of a company. If his annual dividend is Rs 800, find:

(i) The market value of each share.

(ii) The rate percent which he earns on his investment.

(i) Investment = Rs 10000

Face value of each share = Rs 100

Rate of dividend = 10%

Annual dividend = Rs 800

4. At what price should a 9% Rs 100 share be quoted when the money is worth 6%?

If interest is 6 then investment = rs 100

And if interest is 9, then investment = Rs (100 × 9)/6

= Rs 150

Market value of each share = Rs 150

5. By selling at Rs 92, some 2.5% Rs 100 shares and investing the proceeds in 5% Rs 100 shares at Rs 115, a person increased his annual income by Rs 90. Find:

(i) the number of shares sold.

(ii) the number of shares purchased.

(iii) the new income.

(iv) the rate percent which he earns on his investment.

Rate of dividend = 2.5 % and market price = Rs 92

Let number of shares purchased = x

Selling price of x shares = 92x

Income from investing ₹ x = (92x × 2.5)/92

= (92x × 25)/(92 × 10) = 5/2x

Again by investing 92x in 5% at ₹ 115 the dividend = (92x × 5)/115 = 4x

Difference = 4x – 5/2x = 3/2x

∴ 3/2x = 90

⇒ x = (90 × 2)/3 = 60

(i) ∴ No. of shares = 60

(ii) No. of shares sold = 92x/115

= (92 × 60)/115 = 48

(iii) New income = 4x = 4 × 60 = ₹ 240

(iv) rate percent interest on investment = (5 × 100)/115

= 100/23 = 4.35%

6. A man has some shares of Rs. 100 per value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% Rs 50 shares at a premium of Rs 10. This transaction decreases his income from dividends by Rs. 120. Calculate:

(i) the number of shares before the transaction.

(ii) the number of shares he sold.

(iii) his initial annual income from shares.

Let no. of shares = x

Value of x shares = x × 100

= 100x

7. Divide Rs 101520 into two parts that if one part is invested in 8% Rs 100 shares at 8% discount and the other in 9% Rs 50 shares at 8% premium, the annual incomes are equal.

Total investment = Rs 101520

Let investment in first part = x

And in second part = (101520 – x)

Market value of first kind of shares = Rs 100 – Rs 8 = Rs 92

And rate of dividend = 8%

∴ Dividend = (x × 8)/92 = Rs 2x/23

Market value of second kind = (101520 – x)

Rate of dividend = 9%

And market price = Rs (100 + 8)/100 × 50

= 108/100 × 50 = Rs 54

∴ Dividend = (101520 – x) ×9/(2 × 54)

= (101520 – x)/12

∴ According to the sum 2x/23 = (101520 – x)/12

⇒ 24x = 101520 × 23 – 23x

⇒ 24x + 23x = 101520 × 23

⇒ 47x = 101520 × 23

∴ x = (101520 × 23)/47

= 49680

∴ Investment of first part = Rs 49680 and in second part

= Rs 101520 – Rs 49680 = Rs 51840

8. A man buys Rs 40 shares of a company which pays 10% dividend. He buys the shares at such a price that his profit is 16% on his investment. At what price did he buy each share ?

Face value of each share = Rs 40

Dividend = 10%

Gain on investment = 10%

So, the dividend on Rs. 40 = (40 ×10)/100 = Rs 4

Now, Rs 16 is interest on the market value = Rs 100

Hence,

Market value if interests is Rs 4 = (100 × 4)/16

= Rs 25

9. A person invested 20%, 30% and 25% of big savings shares at per values of three different companies A, B and c which declare dividends  of 10%, 12% and 15% respectively. If his total income on account of dividends Rs 4675, find his savings and the amount which he invested in buying shares of each company.

Investment in 3 companies A, B and C = 20%, 30% and 25%

Let total investment = Rs 100

∴ Investment in A company = Rs 20

Rate of dividend = 10%

∴ Dividend = Rs (20 × 10)/100 = Rs 2

Investment in B company = Rs 30.

Rate of dividend = 12%

∴ Dividend = Rs (30 × 12)/100

= Rs 36/10 = Rs 3.60

Investment in company = Rs 25

Rate of dividend = 25%

∴ Dividend = Rs (25 × 15)/100

= Rs 375/100 = Rs 3.75

Total dividend = Rs 2 + 3.60 + 3.75

= Rs 9.35

If dividend is Rs 9.35, then total savings = Rs 100

If dividend is Rd 4675, then total savings = (4675 × 100)/9.35

= (4675 × 100 × 100)/935

= Rs 50000

And amount of investment in shares of A company = Rs 5000 × 20/100

= Rs 10000

Amount of investment in B company = Rs 50000 × 30/100

= Rs 15000

And amount of investment in C company = Rs 50000 ×25/100

= Rs 12500

10. Virat and Dhoni invest ₹36000 each in buying shares of two companies. Virat buys 15% ₹40 shares at a discount of 20%, while Dhoni buys ₹ 75 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Dhoni’s company.

In the first case:

Investment made by Virat = Rs 36000

And market value at a discount of 20% = Rs 40 × 80/100

= Rs 32

∴ Total face value = Rs (36000 × 40)/32

= Rs 45000

Rate of dividend = 15%

∴ Total dividend = Rs (45000 × 15)/100

= Rs 6750

In second case,

Investment = Rs 36000

Dividend of Dhoni = Rs 6750

Face value of each share = Rs 75

And market value at premium of 20%

= Rs 75 × 120/100 = Rs 90

Face value = 36000 × 75/90

= Rs 30000

∴ Rate of dividend = (6750 × 100)/30000 %

= 45/2%

= 22.5%

The solutions provided for Chapter 3 Shares and Dividend of ML Aggarwal Textbook. This solutions of ML Aggarwal Textbook of Chapter 3 Shares and Dividend contains answers to all the exercises given in the chapter. These solutions are very important if you are a student of ICSE boards studying in Class 10. While preparing the solutions, we kept this in our mind that these should based on the latest syllabus given by ICSE Board.

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