# ICSE Solutions for Selina Concise Chapter 3 Shares and Dividend Class 10 Maths

**Exercise 3(A) **

**1. How much money will be required to buy 400, Rs.12.50 shares at a premium of Rs.1?**

**Solution**

Given,

The number of shares required to be bought = 400

And, Rs 12.50 shares at a premium of Rs 1 means;

Nominal value of the share is Rs. 12.50

And its market value = Rs 12.50 + Rs 1 = Rs 13.50

So, the money required to buy 1 share = Rs 13.50

Thus,

The money required to buy 400 shares = 400 × Rs 13.50 = Rs 5400

**2. How much money will be required to buy 250, Rs.15 shares at a discount of Rs.1.50?**

**Solution**

The number of shares to be bought is 250.

And, Rs 15 shares at a discount of Rs 1.50 means

Nominal value of the share is Rs 15 and

Its market value = Rs 15 – Rs 1.50 = Rs 13.50

Thus,

The money required to buy 250 shares = 250 × Rs 13.50 = Rs 3375

**3. A person buys 120 shares at a nominal value of Rs 40 each, which he sells at Rs 42.50 each. Find his profit and profit percent.**

**Solution**

Given,

The nominal value of each share is Rs 40

So, the nominal value of 120 shares = Rs 40 × 120 = Rs 4,800

And, the market value of 120 shares = Rs 42.50 × 120 = Rs 5,100

Thus, his profit = Rs 5,100 – Rs 4,800 = Rs 300

And the profit percentage is given by,

Profit (%) = 300/4800 ×100 = 6.25 %

**4. Find the cost of 85 shares of Rs 60 each when quoted at Rs 63.25.**

**Solution**

Given,

Market value of 1 share = Rs 63.25

So, the market value of 85 shares = Rs 63.25 × 85

= Rs 5,376.25

**5. A man invests Rs800 in buying Rs5 shares and when they are selling at a premium of Rs1.15, he sells all the shares. Find his profit and profit percent.**

**Solution**

Nominal value of 1 share = Rs 5

Market value 1 share = Rs 5 + Rs 1.15 = Rs6.15

Total money invested = Rs 800

So, the number of shares purchased = 800/5 = 160

And,

Market value of 160 shares = 160 × 6.15= Rs 984

Thus, his profit = Rs 984 – Rs 800 = Rs 184

And the profit percentage is given by

Profit (%) = 184/800 ×100 = 23 %

**6. Find the annual income derived from 125, Rs.120 shares paying 5% dividend.**

**Solution**

Given,

The nominal value of 1 share = Rs 120

So, the nominal value of 125 shares = 125 × Rs 120 = Rs 15,000

Now,

Dividend = 5 % of Rs 15,000

⇒ 5/100 ×15000 = Rs 750

Thus, the annual income is Rs 750

**7. A man invests Rs 3,072 in a company paying 5% per annum, when its Rs 10 share can be bought for Rs 16 each. Find:**

**(i) his annual income**

**(ii) his percentage income on his investment.**

**Solution**

Given,

Market value of 1 share = Rs 16

Nominal value of 1 share= Rs 10

And the money invested = Rs3,072

So, the number of shares purchased = 3072/16 = 192

And, the nominal value of 192 shares = Rs 10 × 192 = Rs 1,920

**(i)** The annual income = 5% of Rs 1,920

= 5/100 x 1920

(ii) Income % = 96/3072 × 100 = 3.125%

**Exercise 3(B)**

**1. A man buys 75, Rs 100 shares paying 9 percent dividend. He buys shares at such a price that he gets 12 percent of his money. At what price did he buy the shares?**

**Solution**

Given,

Nominal value of 1 share = Rs100

So, the nominal value of 75 shares = 100 × 75 = Rs 7,500

And, Dividend % = 9 %

Thus, dividend = 9 % of Rs 7,500

= 9/100 × Rs 7,500 = Rs 675

Let’s consider the market price of 1 share = Rs y

Then the market price of 75 shares = Rs 75y

And, Profit % on investment = 12%

12% of 75y = Rs 657

12/100 × 75y = Rs 657

y = Rs 75

∴ the price of his shares is Rs 75 each

**2. By purchasing Rs 25 gas shares for Rs 40 each, a man gets 4 percent profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares?**

**Solution**

Given,

Nominal value of 1 share = Rs 25

Market value of 1 share = Rs 40

And, the profit% on investment = 4%

Then profit on 1 share = 4% of Rs 40 = Rs 1.60

Thus,

Dividend % = 1.60/25 × 100 = 6.4%

Next,

If the number of shares purchased = 60

Then, the dividend on 60 shares = 60 × Rs 1.60 = Rs 96

**3. Hundred rupee shares of a company are available in the market at a premium of Rs 20. Find the rate of dividend given by the company, when a man’s return on his investment is 15%.**

**Solution**

Given,

Nominal value of 1 share = Rs 100

And the market value of 1 share = Rs100 + Rs 20 = Rs120 (as the premium is Rs 20)

Also given, the profit % on investment of 1 share = 15%

Then profit = 15% of Rs 120 = Rs 18

∴ Dividend % = 18/100 × 100 = 18%

**4. Rs 50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20 percent.**

**Solution**

Given,

Nominal value of 1 share = Rs 50

Discount on each share = 10%

So, the market value of 1 share = Rs50 – 10% of Rs50

= Rs 50 – Rs 5 = Rs 45

Also given, Profit % on investment = 20%

Then the profit on 1 share = 20% of Rs 45 = Rs 9

∴ Dividend % = 9/50 × 100 = 18 %

**5. A company declares 8 percent dividend to the shareholders. If a man receives Rs 2,840 as his dividend, find the nominal value of his shares.**

**Solution**

Given,

Dividend % = 8 %

And, the dividend is Rs 2,840

Let the nominal value of shares be Rs y

Then,

8% of y = Rs 2,840

(8/100) × y = Rs 2,840

y = Rs 35,500

Thus, the nominal value of the man’s share is Rs 35,500

**6. How much should a man invest in Rs 100 shares selling at Rs 110 to obtain an annual income of Rs 1,680, if the dividend declared is 12%?**

**Solution**

From the question,

Nominal value of 1 share = Rs100

And, the market value of 1 share = Rs 110

Let the number of shares purchased = n

Then the nominal value of n shares = Rs (100n)

Dividend % = 12%

Given that the dividend = Rs1,680

12 % of 100n = Rs 1,680

12/100 × 100n = Rs 1680

So, the market value of 140 shares = 140 × 110 = Rs 15,400

Therefore the investment of the man should be Rs 15,400

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

**Solution**

Given,

Nominal value of 1 share = Rs60

Market value of 1 share = Rs 60 + 25% of Rs 60

= Rs 60+ Rs 15= Rs 75

Let the number of shares purchased be n

Then, the nominal value of n shares = Rs (60n)

Dividend % = 11.2%

Given that the dividend = Rs 1,680

So, 11.2% of 60n = Rs 1,680

11.2/100 × 60n = Rs 1,680

Then, the market value of 250 shares will be = 250 × 75 = Rs 18,750

∴ the investment of Rakesh should be Rs 18,750

**8. A man buys 400, twenty-rupee shares at a premium of Rs 4 each and receives a dividend of 12%. Find:**

**(i) the amount invested by him.**

**(ii) his total income from the shares.**

**(iii) percentage return on his money.**

**Solution**

Given,

The nominal value of 1 share = Rs 20

Market value of 1 share = Rs 20 + Rs 4 = Rs 24

No. of shares purchased = 400

Nominal value of 400 shares = 400 × 20 = Rs 8,000

**(i)** Market value of 400 shares = 400 × 24 = Rs 9,600

**(ii) **Dividend% = 12%

Dividend = 12% of Rs 8,000

= 12/100 x Rs 8,000 = Rs 960

Thus, the total income from the shares is Rs 960

**(iii)** Percentage return on his money is

Return % = income/investment ×100

= (960/9600) × 100 = 10%

**9. A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% on his money. Calculate:**

**(i) the amount invested by him.**

**(ii) the rate of dividend paid by the company.**

**Solution**

Given,

The nominal value of 1 share = Rs 20

Market value of 1 share = Rs20 – (20% of Rs 20)

= Rs 20 – Rs 4 = Rs 16

Number of shares purchased = 400

Nominal value of 400 shares = 400 × 20 = Rs 8,000

(i) Market value of 400 shares = 400 × 16 = Rs 6,400

(ii) Return% = 12%

Income = 12% of Rs 6,400

= 12/100 × Rs 6,400 = Rs 768

(iii) The rate of dividend is

Dividend % = (income/ nominal value) × 100

= (768/ 8000) × 100 = 9.6 %

**10. A company, with 10,000 shares of Rs 100 each, declares an annual dividend of 5%.**

**(i) What is the total amount of dividend paid by the company?**

**(ii) What should be the annual income of a man who has 72 shares in the company?**

**(iii) If he received only 4% of his investment, find the price he paid for each share.**

**Solution**

Given,

Nominal value of 1 share = Rs100

Then, nominal value of 10,000 shares =10,000 × Rs 100 = Rs 10,00,000

**(i)** Dividend %= 5%

Dividend = 5% of Rs 10,00,000

= 5/100 × Rs 10,00,000 = Rs 50,000

Thus, a dividend amount of Rs 50,000 is paid by the company.

**(ii)** Nominal value of 72 shares = Rs100 × 72 = Rs7,200

Dividend = 5% of Rs7,200

= 5/100 × Rs 7,200 = Rs 360

Thus, the annual income of the man is Rs 360

**(iii) **Let’s consider the market value of 1 share = Rs y

Then market value of 10,000 shares = Rs (10,000y)

And the return% = 4%

So, 4% of Rs (10,000y) = Rs 50,000

= 4/100 × 10,000y = Rs 50,000

y = Rs 125

Thus, the price for each share is Rs 125

**Exercise 3(C)**

**1. By investing Rs.45,000 in 10% Rs.100 shares, Sharad gets Rs.3,000 as dividend. Find the market value of each share.**

**Solution**

We know that,

Annual income from 1 share = 10% of Rs 100 = Rs 10

Given, the total income = Rs 3000 (as dividend)

Hence, The number of shares bought = Total annual income/ Annual income from 1 share

= 3000/10 = 300

∴ The market value of one share = Total investment/ Number of shares

= 4500/300 = Rs 150

**2. Mrs. Kulkarni invests Rs.1, 31,040 in buying Rs.100 shares at a discount of 9%. She sells shares worth Rs.72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss on the whole. **

**Solution**

Given,

Investment = Rs 1,31,040

Nominal value of 1 share = Rs 100

Discount = 9% of Rs 100 = Rs 9

So, the market value of 1 share = Rs 100 – Rs 9 = Rs 91

Then, the number of shares purchased = Investment/ market value of 1 share

= 1,31,040/ 91 = 1440

Number of shares worth Rs 72,000 = 72,000/100 = 720

Now, Mrs. Kulkarni sells 720 shares at a premium of 10%

Then, the market value of 1 share = Rs 100 + Rs 10 = Rs 110

So, the selling price of 720 shares = 720 × Rs 110

The number of remaining shares = 1440 – 720 = 720

And, she sells 720 shares at a discount of 5%

Now, the market value of 1 share = Rs 100 – Rs 5 = Rs 95

The selling price of 730 shares = 720 × Rs 95 = Rs 68,400

Total selling price = Rs(79,200 + 68,400) = Rs 1,47,600

Thus, the total gain = Total selling price – Total investment

= Rs (1,47,600 – 1,31,040)

= Rs 16560

**3. A man invests a certain sum on buying 15% Rs.100 shares at 20% premium. Find :**

**(i) His income from one share**

**(ii) The number of shares bought to have an income, from the dividend, Rs.6480**

**(iii) Sum invested**

**Solution**

(i) Dividend on one share = 15% of Rs 100

= Rs (15/100 ×100) = Rs 15

Hence, the income from one share is Rs 15

(ii) Number of shares bought by the man = annual income/ dividend on one share

= 6480/ 15 = Rs 432

(iii) Given that the man bought shares of Rs 100 at 20% premium, the market value of one share

= Rs (1 + 20/100) × 100

= Rs (120/100 ×100) = Rs 120

His total investment = number of shares x market value of one share

= 432 × Rs 120

= Rs 51,840

**4. Gagan invested 80% of his savings in 10% Rs.100 shares at 20% premium and the rest of his savings in 20% Rs.50 shares at Rs.20% discount. If his incomes from these shares is Rs.5,600 calculate:**

**(i) His investment in shares on the whole**

**(ii) The number of shares of first kind that he bought**

**(iii) Percentage return, on the shares bought on the whole.**

**Solution**

(i) Let’s assume the total savings be Rs x (which is the investment)

For the 1^{st} part – 80% of his savings

Nominal value of each share = Rs 100

Market value of each share = 100 + 20% of Rs 100 = 100 + 20 = Rs 120

So, the number of shares bought will be = 0.8x/120

Dividend on each share = 10% of 100 = Rs 10

Hence, the total dividend = 10 ×(0.8x/120) = Rs 0.8x/12

Now, the 2^{nd} part (remaining 20% of savings)

Nominal value of each share = Rs 50

Market value of each = 50 – 20% Rs 50 = 50 – 10 = Rs 40

So, the number of shares bought = 0.2x/ 40

Dividend on each share = 20% of 50 = Rs 10

Hence, the total dividend = 10 × 0.2x/40 = Rs 0.2x/4

Given that dividend (incomes) from both the investments are Rs 5600

So, we have

Rs 0.8x/12 + Rs 0.2x/4 = 5600

(0.8x + 0.6x)/12 = 5600

x = (5600 × 12)/1.4

x = 48,000

∴ the investment in shares together as his savings is Rs 48,000

**(ii)** Now, the number of shares bought = 0.8x/120 = (0.8 ×48,000)/ 120 = Rs 320

**(iii)** The total dividend or the return = 0.8x/12 + 0.2x/4

= 0.8(48,000)/12 + 0.2(48,000)/4

Thus, the return percentage = 5600/48000 ×100

**5. Aishwarya bought 496, Rs.100 shares at Rs.132 each, find:**

**(i) Investment made by her**

**(ii) Income of Aishwarya from these shares, if the rate of dividend is 7.5%.**

**(iii) How much extra must Aishwarya invest in order to increase her income by Rs.7,200**

**Solution**

Given,

**(i)** The nominal value of each share = Rs 100

Market price of each share = Rs 132

Number of shares bought = 496

So, the investment made by her = 496 × Rs 132 = Rs 65,472

**(ii)** Dividend on 1 share = 7.5% of Rs 100 = Rs 7.5

Thus, the income of Aishwarya from these shares = 496 × 7.5 = Rs 3,720

**(iii)** If she wants to increase her income by Rs 7,200

Then the number of shares she should buy = increase in the income/ income of one share

= 7,200/7.5 = 960

∴ she should invest an extra of = 960 × Rs 132 = Rs 1,26,720

**6. Gopal has some Rs.100 shares of company A, paying 10% dividend. He sells a certain number of these shares at a discount of 20% and invests the proceeds in Rs.100 shares at Rs.60 of company B paying 20% dividend. If his income, from the shares sold, increases by Rs.18,000, find the number of shares sold by Gopal.**

**Solution**

Given,

The nominal value of each share = Rs 100

Rate of dividend = 10%

Dividend on each share = 10% of Rs 100 = Rs 10

Then, the dividend on x shares will be Rs 10x

Selling price of each share = Rs 100 = 20% of Rs 100 = Rs 80

And, the amount obtained on selling x shares = Rs 80x

Given that, the proceeds are invested in Rs 100 shares at Rs 60 of company B paying 20% dividend

Now,

Nominal value of each share = Rs 100

Market value of each share = Rs 60

So, the number of shares bought by the man = amount obtained/ Market value of each share

= 80x/60 = 4x/3

Dividend on each share = 20% of Rs 100 = Rs 20

So the total dividend received = Divided on each share x number of shares

= 20 × 4x/3 = 80x/3

Given, the increase in the income = Rs 18,000

Thus,

80x/3 – 10x = 18,000

50x/3 = 18,000

x = Rs 1080

∴ the number of shares sold by Gopal is Rs 1080

**7. A man invests a certain sum of money in 6% hundred-rupee shares at Rs.12 premium. When the shares fell to Rs.96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at Rs.8. If the change in his income is Rs.540, Find the sum invested originally**

**Solution**

Let’s assume the original sum invested to be Rs x

Then the number of Rs 100 shares purchased at premium of Rs 12 will be

= x/(100 + 12) = x/112

Given,

The income per original share is 6% = Rs 6

So, the total income = (Number of shares) x (earning per share)

= (x/112) × 6 = 3x/56

Proceeds from the sale of original shares at Rs 96 per share

= (number of shares) × 96 = x/112 × 96 = 6x/7

Number of Rs 10 shares purchased at Rs 8 per share from the proceeds of original shares

= (Proceeds from sale of original shares)/8 = (6x/7)/8 = 3x/28

Income per new share of Rs 10 at 10% = 10/100 × 10 = Rs 1

Thus, the total income from the new shares = Number of shares x income per share

= 3x/28 ×1 = 3x/28

The change in income is Rs 540 (given)

Income from old shares – Income from new shares = Rs 540

So,

540 = 3x/28 – 3x/56 = 3x/56

x = 540/(3/56) = 10, 080

∴ the original sum invested is Rs 10,080

**8. Mr. Gupta has a choice to invest in ten-rupee shares of two firms at Rs13 or at Rs16. If the first firm pays 5% dividend and the second firm pays 6% dividend per annum, find:**

**(i) which firm is paying better.**

**(ii) if Mr. Gupta invests equally in both the firms and the difference between the returns from them is Rs 30, find how much, in all, does he invest.**

**Solution**

**(i)** The first firm:

Nominal value of 1 share = Rs 10

Market value of 1 share = Rs 13

Dividend = 5% of Rs 10 = Rs 0.50

Thus, the income % = Income/ Investment ×100

= 0.50/13 ×100 = 3.846 %

Now,

The second firm:

Nominal value of 1 share = Rs 10

Market value of 1 share = Rs 16

Dividend % = 6 %

Thus, income % = income/ investment ×100

= 0.60/ 16 ×100

= 3.75 %

∴ the first firm is paying better than second firm

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

For 1^{st} firm

Number of shares purchased = y/13 shares

Total dividend = Rs 0.50 × y/13 = Rs y/26

For 2^{nd} firm

Number of shares purchased = y/16 shares

Total dividend = Rs 0.60 × y/16 = Rs 3y/80

Given the difference of both dividend = Rs 30

y/26 – 3y/80 = Rs 30

y/1040 = Rs 30

y = Rs 30 × 1040 = Rs 31,200

∴ total money invested in both firm = Rs 31,200 × 2

= Rs 62,400

**9. Ashok invested Rs.26,400 in 12%, Rs.25 shares of a company. If he receives a dividend of Rs.2,475, find the:**

**(i) number of shares he bought.**

**(ii) market value of each share. **

**Solution**

(i) Given, total dividend = Rs 2,475

So, the dividend on each share = 12% of Rs 25 = 12/100 × Rs 25 = Rs 3

Thus, the number of shares bought = Total dividend/ Dividend on 1 share

= 2475/3 = 825

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

∴ market value of each share = total investment/ number of shares = 26400/825 = Rs 32

**10. A man invested Rs45,000 in 15% Rs100shares quoted at Rs125. When the market value of these shares rose to Rs140, he sold some shares, just enough to raise Rs8,400. Calculate:**

**(i)the number of shares he still holds;**

**(ii)the dividend due to him on these remaining shares.**

**Solution**

(i) Total investment = Rs 45,000

And the market value of 1 share = Rs 125

Thus, the number of shares purchased = 45000/125 = 360 shares

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

Now, let the number of shares sold be n

Then, the sale price of these n shares is = Rs 8,400

So,

n = 8400/140 = 60 shares

Thus, the number of shares he still holds is 360 – 60 = 300

(ii) Nominal value of 300 shares = Rs 100 × 300 = Rs 30,000

And, dividend% = 15%

Dividend = 15% of Rs 30,000

= 15/100 × Rs 30,000 = Rs 4,500