Shares & Dividends — Test Yourself

A company pays 18% dividend and its ₹ 100 share is available at a premium of 20%. The number of shares bought for ₹ 7,200 is :

1. 1080

2. 90

3. 60

4. 540

Answer

N.V. of share = ₹ 100

Premium = 20%

M.V. of share = N.V. + premium

= ₹ 100 + 20%

= ₹ 100 + $\dfrac{20}{100} \times 100$

= ₹ 100 + ₹ 20 = ₹ 120.

No. of shares bought = $\dfrac{\text{Sum invested}}{\text{M.V.}} = \dfrac{7200}{120}$ = 60.

Hence, Option 3 is the correct option.

100, ₹ 100 shares (paying 10% dividend) are brought at a discount of ₹ 20 and another 100, ₹ 100 shares (paying 10% dividend) are brought at ₹ 120. The total dividend earned is :

1. ₹ 00

2. ₹ 2,000

3. ₹ 400

4. ₹ 2,400

Answer

For 1st share :

N.V. = ₹ 100

Dividend % = 10%

No. of shares = 100

Dividend = No. of shares × Dividend % × N.V.

= 100 × 10% × 100

= 100 × $\dfrac{10}{100} \times$ 100

= ₹ 1000.

For 2nd share :

N.V. = ₹ 100

Dividend % = 10%

No. of shares = 100

Dividend = No. of shares × Dividend % × N.V.

= 100 × 10% × 100

= 100 × $\dfrac{10}{100} \times$ 100

= ₹ 1000.

Total dividend = ₹ 1000 + ₹ 1000 = ₹ 2000.

Hence, Option 2 is the correct option.

The money required, to buy 80 shares, each of ₹ 60 and quoted at ₹ 70, is :

1. ₹ 5600

2. ₹ 4800

3. ₹ 80 × 60 × 70

4. ₹ 4200

Answer

Given,

M.V. of share = ₹ 70

No. of shares = 80

Sum required = No. of shares × M.V.

= 80 × ₹ 70 = ₹ 5600.

Hence, Option 1 is the correct option.

₹ 20,000 is spent in buying ₹ 50 shares with dividend 5%. The dividend earned is :

1. ₹ 1000

2. ₹ 200

3. ₹ 500

4. ₹ 2000

Answer

Given,

N.V. of each share = ₹ 50

Sum invested = ₹ 20,000

No. of shares bought = $\dfrac{\text{Sum invested}}{\text{N.V. of each share}} = \dfrac{20,000}{50}$ = 400.

By formula,

Dividend = No. of shares × Dividend % × N.V.

= 400 × 5% × 50

= $400 \times \dfrac{5}{100} \times 50$

= ₹ 1000.

Hence, Option 1 is the correct option.

Each of ₹ 500 shares is available at a discount of ₹ 100. If the dividend on these shares is 8%, the income percent is :

1. 8%

2. 15%

3. 5%

4. 10%

Answer

Given,

N.V. of each share = ₹ 500

Discount = ₹ 100

M.V. = N.V. - Discount

= ₹ 500 - ₹ 100 = ₹ 400.

Dividend = 8%

Let income percent be r%.

By formula,

Income percent on M.V. = Dividend on N.V.

Substituting values we get :

r% of 400 = 8% of 500

$\Rightarrow \dfrac{r}{100} \times 400 = \dfrac{8}{100} \times 500 \\[1em] \Rightarrow 4r = 40 \\[1em] \Rightarrow r = \dfrac{40}{4} = 10$

Hence, Option 4 is the correct option.

Investing in 16% ₹ 100 shares at ₹ 80 or in 20% ₹100 shares at ₹120.

Assertion (A): It is better to invest in 16% ₹ 100 shares at ₹ 80.

Reason (R): Return % from the shares = $\dfrac{\text{Income}}{\text{Investment}} \times 100$.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

Answer

Both A and R are true and R is correct reason for A.

Reason

Face value of the 1st share = ₹ 100

Dividend rate = 16%

Market value = ₹ 80

Dividend (or income) per share = Dividend rate x face value of each share

= 16% of 100 = $\dfrac{16}{100}$ x 100 = ₹ 16

Rate of return = $\dfrac{\text{Annual income on 1 share}}{\text{Investment on 1 share}}$ x 100

= $\dfrac{16}{80}$ x 100 = 20%

Face value of second share = ₹ 100

Dividend rate = 20%

Market value = ₹ 120

Dividend (or income) per share = Dividend rate x face value of each share

= 20% of 100 = $\dfrac{20}{100}$ x 100 = ₹ 20

Rate of return = $\dfrac{\text{Annual income on 1 share}}{\text{Investment on 1 share}}$ x 100

= $\dfrac{20}{120}$ x 100 = 16.66%

The scheme that offers a higher rate of return is considered better. And, rate of return in first scheme is 20% and that of second scheme is 16.66%.

So, Assertion (A) is true.

Rate of return = $\dfrac{\text{Annual income on 1 share}}{\text{Investment on 1 share}}$ x 100

= $\dfrac{\text{Income}}{\text{Investment}}$ x 100

The given formula for rate of return is true.

So, Reason (R) is true.

Hence, option 3 is correct.

₹ 50 shares of a company are bought by John at 20% discount and sold at the gain of 25%.

Assertion (A): The net gain on each share is 5%.

Reason (R): The selling price of each share = $₹ 50 \times \dfrac{80}{100} \times \dfrac{125}{100}$.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

Answer

A is false, R is true.

Reason

Face value of share = ₹ 50

Discount = 20%

Discounted value = 20% of ₹ 50 = $\dfrac{20}{100} \times 50$ = ₹ 10

Discounted price = ₹ 50 - ₹ 10 = ₹ 40

Gain = 25%

Selling price = ₹ 40 + 25% of ₹ 40

= ₹ 40 + $\dfrac{25}{100} \times 40$ = ₹ (40 + 10) = ₹ 50

Gain = ₹ 50 - ₹ 40 = ₹ 10

Gain % = $\dfrac{\text{Gain}}{\text{CP}} \times 100$

= $\dfrac{10}{40} \times 100$ = 25%

So, Assertion (A) is false.

As per the Reason (R),

The selling price of each share = $₹ 50 \times \dfrac{80}{100} \times \dfrac{125}{100}$

$= ₹ (50 \times 0.8 \times 1.25) \\[1em] = ₹ 50$

This is equal to the selling price computed above.

So, Reason (R) is true.

Hence, option 2 is correct.

₹ 2,250 is invested in buying ₹ 50 shares available at 10% discount and the dividend paid by the company is 12%.

Statement (1) : Number of shares bought = $\dfrac{2,250}{45}$ = 50

Statement (2) : Total dividend paid by the company = (12% of ₹ 50) x 50

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Both the statements are true.

Reason

Total investment = ₹ 2,250

Discount on shares = 10%

Dividend rate = 12%

Face value of each share = ₹50

Discounted value = 10% of ₹50

= $\dfrac{10}{100} \times 50$ = ₹ 5

Discounted price = ₹ 50 - 5 = ₹ 45

And, number of shares = $\dfrac{\text{Total Investment}}{\text{Market Value of 1 share}}$

= $\dfrac{2,250}{45}$ = 50

So, statement 1 is true.

The annual dividend = number of shares x rate of dividend x face value of one share

= 50 x 12% x 50

= (12% of ₹ 50) x 50

So, statement 2 is true.

Hence, option 1 is correct.

100 shares are bought at ₹ 60 per share and the dividend received is ₹ 600.

Statement (1) : Rate of return x ₹ 60 x 100 = ₹ 600

Statement (2) : Rate of return x Market value = Dividend received on each share

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Both the statements are true.

Reason

Number of shares bought = 100

Price per share = ₹60

Total dividend received = ₹600

Rate of return = $\dfrac{\text{Annual income}}{\text{Investment}}$

= $\dfrac{\text{Annual income}}{\text{No. of shares} \times \text{price per share}}$

⇒ Rate of return = $\dfrac{600}{100 \times 60}$

⇒ Rate of return x 60 x 100 = 600

So, statement 1 is true.

Rate of return = $\dfrac{\text{Annual income}}{\text{No. of shares} \times \text{price per share}}$

⇒ Rate of return x Price per share = $\dfrac{\text{Annual income}}{\text{No. of shares}}$

⇒ Rate of return x Market value = Dividend received on each share

So, statement 2 is true.

Hence, option 1 is correct.

Ankit had the option of investing in company A, where 7% ₹ 100 shares are available at ₹ 120 or in company B, where 8%, ₹ 1000 shares are available at ₹ 1620.

Statement (1) : Investment in company B is better than company A.

Statement (2) : Yield % of company B is better than in company A.

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

For company A :

Dividend = 7%

N.V. = ₹ 100

M.V = ₹ 120

Dividend per share = 7% of N.V.

= $\dfrac{7}{100} \times 100$ = ₹ 7

⇒ Rate of return = $\dfrac{\text{Dividend earned on 1 share}}{\text{Market Value of one share}} \times 100$

= $\dfrac{7}{120} \times 100$ = 5.83%

For company B :

Dividend = 8%

N.V. = ₹ 1000

M.V = ₹ 1620

Dividend per share = 8% of N.V.

= $\dfrac{8}{100} \times 1000$ = ₹ 80

⇒ Rate of return = $\dfrac{\text{Dividend earned on 1 share}}{\text{Market Value of one share}} \times 100$

= $\dfrac{80}{1620} \times 100$ = 4.94%

Investment in company B is better than A. This is false, because A gives higher yield.

So, statement 1 is false.

Yield of company B is better than A.

Company A gives better return that is 5.83%.

So, statement 2 is false.

Hence, option 2 is correct.

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

Answer

Let market value of share be x.

∴ No. of share = $\dfrac{45000}{x}$

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

$\therefore 3000 = \dfrac{45000}{x} \times \dfrac{10}{100} \times 100 \\[1em] \Rightarrow x = \dfrac{450000}{3000} \\[1em] \Rightarrow x = 150$

Hence, M.V. of share = ₹ 150.

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

Answer

Investment = ₹ 1,31,040

N.V. of 1 share = ₹ 100

Discount = 9% of ₹ 100 = ₹ 9

∴ M.V. of 1 share = ₹ 100 - ₹ 9 = ₹ 91

∴ No. of shares purchased = $\dfrac{\text{Investment}}{\text{M.V. of 1 share}} = \dfrac{131040}{91}$ = 1440

No. of shares worth ₹ 72,000 = $\dfrac{72000}{100} = 720$

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

M.V. of 1 share = ₹ 100 + ₹ 10 = ₹ 110

∴ Selling price of 720 shares = 720 × ₹ 110 = ₹ 79,200

No. of remaining shares = 1440 - 720 = 720.

She sells 720 shares at a discount of 5%

M.V. of 1 share = ₹ 100 - ₹ 5 = ₹ 95

∴ Selling price of 720 shares = 720 × ₹ 95 = ₹ 68,400

∴ Total selling price = ₹ 79,200 + ₹ 68,400 = ₹ 1,47,600

∴ Total gain = Total selling price - Total investment = ₹ 1,47,600 - ₹ 1,31,040 = ₹ 16,560.

Hence, total gain = ₹ 16,560.

A man invests a certain sum in buying 15% ₹ 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, ₹ 6,480.

(iii) sum invested.

Answer

(i) Dividend on 1 share = $\dfrac{15}{100} \times 100$ = ₹ 15.

Hence, the income from one share is ₹ 15.

(ii) Number of shares bought = $\dfrac{\text{Annual income}}{\text{Div. on 1 share}} = \dfrac{6480}{15} =$ 432.

Hence, the number of shares bought = 432.

(iii) M.V. = ₹ 100 + ₹ $\dfrac{20}{100} \times 100$ = ₹ 100 + ₹ 20 = ₹ 120.

Total investment = No. of shares × M.V. = 432 × ₹ 120 = ₹ 51,840.

Hence, sum invested = ₹ 51,840.

Ashwarya bought 496, ₹ 100 shares at ₹ 132 each. Find :

(i) investment made by her.

(ii) income of Ashwarya from these shares, if rate of dividend is 7.5%

(iii) how much extra must Ashwarya invest in order to increase her income by ₹ 7,200?

Answer

(i) M.V. = ₹ 132

Investment = 496 × ₹ 132 = ₹ 65,472

Hence, investment made by Ashwarya = ₹ 65,472.

(ii) Dividend = No. of shares × Rate of div. × N.V. of 1 share

= 496 × $\dfrac{7.5}{100} \times 100$

= ₹ 3,720.

Hence, income of Ashwarya = ₹ 3,720.

(iii) Dividend on 1 share = 1 × $\dfrac{7.5}{100} \times 100$ = 7.5

No. of shares to buy in order to increase income by 7200 = $\dfrac{7200}{7.5} = 960$

Investment = 960 × 132 = ₹ 1,26,720.

Hence, investment required = ₹ 1,26,720.

Gopal has some ₹ 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 ₹ 100 shares at ₹ 60 of company B paying 20% dividend. If his income, from the shares sold, increases by ₹ 18,000, find the number of shares sold by Gopal.

Answer

Let the number of shares Gopal sold be x.

N.V. = ₹ 100

Rate of dividend = 10%

Dividend = No. of shares × Rate of div. × N.V. of 1 share

= x $\times \dfrac{10}{100} \times 100$

= 10x.

S.P. = ₹ 100 - 20% of ₹ 100

= ₹ 100 - $\dfrac{20}{100} \times 100$

= ₹ 100 - ₹ 20

= ₹ 80.

Amount obtained on selling x shares = ₹ 80x.

The proceeds he invested in ₹ 100 shares at ₹ 60 of company B paying 20% dividend.

N.V. = ₹ 100

M.V. = ₹ 60

No. of shares bought by man = $\dfrac{\text{Amount invested}}{\text{M.V.}} = \dfrac{80x}{60} = \dfrac{4x}{3}.$

Dividend = No. of shares × Rate of div. × N.V. of 1 share

= $\dfrac{4x}{3} \times \dfrac{20}{100} \times 100$

= $\dfrac{80x}{3}$.

Given, increase in income = ₹ 18000

$\therefore \dfrac{80x}{3} - 10x = 18000 \\[1em] \Rightarrow \dfrac{80x - 30x}{3} = 18000 \\[1em] \Rightarrow \dfrac{50x}{3} = 18000 \\[1em] \Rightarrow x = \dfrac{18000 \times 3}{50} \\[1em] \Rightarrow x = 1080.$

Hence, no.of shares sold by Gopal is 1080.

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

Answer

Let sum originally invested be ₹ x,

M.V. of first type of shares = ₹ 100 + ₹ 12 = ₹ 112.

No. of shares = $\dfrac{x}{112}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$= \dfrac{x}{112} \times \dfrac{6}{100} \times 100 \\[1em] = \dfrac{3x}{56}.$

S.P. of shares = ₹ 96 × $\dfrac{x}{112} = \dfrac{96x}{112}$

M.V. of second type of shares = ₹ 8

No. of second type of shares = $\dfrac{\dfrac{96x}{112}}{8} = \dfrac{12x}{112}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$= \dfrac{12x}{112} \times \dfrac{10}{100} \times 10 \\[1em] = \dfrac{6x}{56}.$

Given, change in income = ₹ 540

$\therefore \dfrac{6x}{56} - \dfrac{3x}{56} = 540 \\[1em] \Rightarrow \dfrac{3x}{56} = 540 \\[1em] \Rightarrow x = \dfrac{540 \times 56}{3} = 10,080.$

Hence, sum invested originally = ₹ 10,080.

Mr. Gupta has a choice to invest in ten-rupee shares of two firms at ₹ 13 or at ₹ 16. 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 difference between the returns from them is ₹ 30, find how much, in all, does he invest?

Answer

(i) First firm :

Nominal value of 1 share = ₹ 10

M.V. = ₹ 13

Dividend = 5%

Dividend = 1 × $\dfrac{5}{100} \times 10$ = 0.50

Income% = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{0.5}{13} \times 100$ = 3.846%

Second firm :

Nominal value of 1 share = ₹ 10

M.V. = ₹ 16

Dividend = 6%

Dividend = 1 × $\dfrac{6}{100} \times 10$ = 0.60

Income% = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{0.6}{16} \times 100$ = 3.75%

Hence, first firm pays better.

(ii) Let investment on both firms be ₹ x each.

In first case :

M.V. = ₹ 13

No. of shares = $\dfrac{x}{13}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$= \dfrac{x}{13} \times \dfrac{5}{100} \times 10 \\[1em] = \dfrac{x}{26}.$

In second case :

M.V. = ₹ 16

No. of shares = $\dfrac{x}{16}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$= \dfrac{x}{16} \times \dfrac{6}{100} \times 10 \\[1em] = \dfrac{3x}{80}.$

Given, difference between returns = ₹ 30

$\Rightarrow \dfrac{x}{26} - \dfrac{3x}{80} = 30 \\[1em] \Rightarrow \dfrac{40x - 39x}{1040} = 30 \\[1em] \Rightarrow \dfrac{x}{1040} = 30 \\[1em] \Rightarrow x = 30 \times 1040 = 31,200.$

Total investment = x + x = 2x = 2 x 31200 = ₹ 62,400.

Hence, total investment = ₹ 62,400.

A man invested ₹ 45,000 in 15% ₹ 100 shares quoted at ₹ 125. When the M.V. of these shares rose to ₹ 140, he sold some shares, just enough to raise ₹ 8,400. Calculate :

(i) the number of shares he still holds;

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

Answer

(i) No. of shares = $\dfrac{\text{Investment}}{\text{M.V.}} = \dfrac{45000}{125}$ = 360.

S.P. of one share = ₹ 140,

Hence, shares required to raise ₹ 8400,

= $\dfrac{\text{Money required}}{\text{S.P. of each share}} = \dfrac{8400}{140} = 60.$

Shares left = 360 - 60 = 300.

Hence. no. of shares left = 300.

(ii) Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= 300 × $\dfrac{15}{100} \times 100$

= ₹ 4,500.

Hence, dividend due = ₹ 4,500.

A dividend of 12% was declared on ₹ 150 shares selling at a certain price. If the rate of return is 10%, calculate :

(i) the market value of the shares.

(ii) the amount to be invested to obtain an annual dividend of ₹ 1,350.

Answer

(i) Let M.V. be ₹ x.

We know that,

Rate of dividend × N.V. = Profit (return) % × M.V.

$\Rightarrow \dfrac{12}{100} \times 150 = \dfrac{10}{100} \times x \\[1em] \Rightarrow x = 180.$

Hence, market value of shares = ₹ 180.

(ii) Let amount to be invested be ₹ y.

No. of shares = $\dfrac{y}{180}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$\therefore 1350 = \dfrac{y}{180} \times \dfrac{12}{100} \times 150 \\[1em] \Rightarrow y = 13,500$

Hence, amount to be invested = ₹ 13,500.

Divide ₹50,760 into two parts such that if one part is invested in 8% ₹ 100 shares at 8% discount and the other in 9% ₹ 100 shares at 8% premium, the annual incomes from both the investments are equal.

Answer

Let money invested be ₹ x and ₹ (50760 - x)

In first case :

M.V. = ₹ 100 - $\dfrac{8}{100}$ x 100 = ₹ 100 - ₹ 8 = ₹ 92.

No. of shares = $\dfrac{x}{92}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $\dfrac{x}{92} \times \dfrac{8}{100} \times 100 = \dfrac{2x}{23}$

In second case :

M.V. = ₹ 100 + $\dfrac{8}{100}$ x 100 = ₹ 100 + ₹ 8 = ₹ 108.

No. of shares = $\dfrac{50760 - x}{108}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $\dfrac{50760 - x}{108} \times \dfrac{9}{100} \times 100 = \dfrac{50760 - x}{12}$

Given, annual income are same,

$\therefore \dfrac{2x}{23} = \dfrac{50760 - x}{12} \\[1em] \Rightarrow 24x = 23(50760 - x) \\[1em] \Rightarrow 24x = 1167480 - 23x \\[1em] \Rightarrow 47x = 1167480 \\[1em] \Rightarrow x = \dfrac{1167480}{47} \\[1em] \Rightarrow x = 24,840$

50760 - x = ₹ 50760 - ₹ 24840 = ₹ 25,920.

Hence, money invested in first firm = ₹ 24,840 and in second firm = ₹ 25,920.

Vivek invests ₹ 4,500 in 8%, ₹ 10 shares at ₹ 15. He sells the shares when the price rises to ₹ 30, and invests the proceeds in 12% ₹ 100 shares at ₹ 125. Calculate :

(i) the sale proceeds

(ii) the number of ₹ 125 shares he buys

(iii) the change in his annual income from dividend.

Answer

(i) Investment = ₹ 4,500

M.V. = ₹ 15

No. of shares = $\dfrac{4500}{15}$ = 300.

Given, shares are sold when price rises to ₹ 30,

Sale proceeds = 300 × 30 = ₹ 9,000.

Hence, sale proceeds = ₹ 9,000.

(ii) M.V. of second type of shares = ₹ 125

Investment = ₹ 9,000

No. of shares = $\dfrac{9000}{125}$ = 72.

Hence, no. of ₹ 125 shares = 72.

(iii) Annual income = No. of shares × Rate of div. × N.V. of 1 share

In first case :

Annual income = 300 × $\dfrac{8}{100} \times 10$ = ₹ 240.

In second case :

Annual income = 72 × $\dfrac{12}{100} \times 100$ = ₹ 864.

Difference = ₹ 864 - ₹ 240 = ₹ 624.

Hence, difference in annual income = ₹ 624.

Mr. Parekh invested ₹52,000 on ₹ 100 shares at a discount of ₹ 20 paying 8% dividend. At the end of one year he sells the shares at a premium of ₹ 20. Find :

(i) the annual dividend.

(ii) the profit earned including his dividend.

Answer

(i) M.V. = ₹ 100 - ₹ 20 = ₹ 80.

Investment = ₹52,000

No. of shares = $\dfrac{52000}{80} = 650$

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= 650 × $\dfrac{8}{100} \times 100$

= ₹ 5,200.

Hence, annual dividend = ₹ 5,200.

(ii) S.P. = ₹ 100 + ₹ 20 = ₹ 120.

S.P. of 650 shares = 650 × ₹ 120 = ₹ 78,000

Profit = S.P. - C.P. = ₹ 78,000 - ₹ 52,000 = ₹ 26,000.

Profit + dividend = ₹ 26,000 + ₹ 5,200 = ₹ 31,200.

Hence, profit earned including dividend = ₹ 31,200.

Salman buys 50 shares of face value ₹ 100 available at ₹ 132.

(i) What is his investment?

(ii) If the dividend is 7.5%, what will be his annual income ?

(iii) If he wants to increase his annual income by ₹ 150, how many extra shares should he buy?

Answer

(i) Investment = ₹ 132 × 50 = ₹ 6,600

Hence, Salman's investment = ₹ 6,600.

(ii) Annual income = No. of shares × Rate of div. × N.V. of 1 share

= 50 × $\dfrac{7.5}{100} \times 100$

= ₹ 375.

Hence, annual income = ₹ 375.

(iii) Let no. of shares needed to get income of ₹ 525 (₹ 375 + ₹ 150) be x

Annual income = No. of shares × Rate of div. × N.V. of 1 share

525 = x $\times \dfrac{7.5}{100} \times 100$

x = $\dfrac{525}{7.5}$ = 70.

Extra shares = 70 - 50 = 20.

Hence, Salman should buy 20 extra shares.

Anaya invests a sum of money in ₹ 50 shares, paying 15% dividend quoted at 20% premium. If her annual dividend is ₹ 600, calculate :

(i) the number of shares she bought.

(ii) her total investment.

(iii) the rate of return on her investment.

Answer

(i) Let no. of shares be x.

By formula,

Annual income (or dividend) = No. of shares × Rate of div. × N.V. of 1 share

600 = $x \times \dfrac{15}{100} \times 50$

x = $\dfrac{1200}{15}$ = 80.

Hence, no. of shares = 80.

(ii) M.V. = ₹ 50 + $\dfrac{20}{100} \times 50$ = ₹ 50 + ₹ 10 = ₹ 60

Total investment = No. of shares × M.V. of each share

= 80 × ₹ 60 = ₹ 4,800.

Hence, total investment = ₹ 4,800.

(iii) Annual income = ₹ 600.

Return % = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{600}{4800} \times 100 = 12.5$

Hence, return % = 12.5%.

₹ 100 shares of a company giving 10% dividend, are available at ₹ 150. Mr. Saha invests ₹18,000 to buy these shares. He sells 80% of his shares after one year. Find :

(i) the number of shares he purchased.

(ii) the number of shares he sold

(iii) his annual income from the remaining 20% shares he still holds.

Answer

(i) Given,

Total investment = ₹ 18,000

Market value = ₹ 150

N.V = ₹ 100

By formula,

⇒ Total investment = Number of shares × Market value of one share

⇒ 18000 = Number of shares × 150

⇒ Number of shares = $\dfrac{18000}{150}$

⇒ Number of shares = 120.

Hence, the number of shares Mr.Saha purchased = 120.

(ii) Number of shares sold by Mr Saha = 80% of 120

= $\dfrac{80}{100} \times 120$

= 0.8 × 120

= 96.

Hence, the number of shares Mr.Saha sold = 96.

(iii) Number of shares remaining = Total no. of shares - No. of shares sold = 120 - 96 = 24.

By formula,

Annual income = Number of shares × Rate of dividend × N.V. of 1 share

= 24 × $\dfrac{10}{100} \times 100$

= ₹ 240.

Hence, annual income from remaining shares = ₹ 240.

Mr. Gautam sold a certain number of ₹ 20 shares paying 8% dividend at ₹ 18 and invested the proceed in ₹ 10 shares paying 12% dividend at 50% premium. If the change in his annual income is ₹ 120, find the number of shares sold by Mr. Gautam.

Answer

Let the number of shares Mr. Gautam sold be x.

For initial shares,

N.V. = ₹ 20

Rate of dividend = 8%

By formula,

Annual income (from first investment) = No. of shares × Rate of div. × N.V. of 1 share

= x × $\dfrac{8}{100}$ × 20

= $\dfrac{8x}{5}$

S.P. of each share = ₹ 18.

Amount obtained on selling shares = S.P × No. of shares = ₹ 18x.

The proceeds he invested in ₹ 10 shares at ₹ 15, paying 12% dividend.

N.V. = ₹ 10

Premium = 50% of ₹ 10 = $\dfrac{50}{100} \times 10$ = 5

M.V. = N.V. + Premium = ₹ 10 + 5 = ₹ 15

Number of shares = $\dfrac{\text{Total investment}}{\text{Market value of each share}}$

$= \dfrac{18x}{15} = \dfrac{6x}{5}$

The change in Mr. Gautam's annual income = ₹ 120

By formula,

Annual income (from second investment) = No. of shares × Rate of div. × N.V. of 1 share

= $\dfrac{6x}{5} \times \dfrac{12}{100} \times 10$

= $\dfrac{720x}{500} = \dfrac{36x}{25}$

Given, change in income = ₹ 120

$\therefore \dfrac{8x}{5} - \dfrac{36x}{25} = 120 \\[1em] \Rightarrow \dfrac{40x - 36x}{25} = 120 \\[1em] \Rightarrow \dfrac{4x}{25} = 120 \\[1em] \Rightarrow x = \dfrac{120 \times 25}{4} \\[1em] \Rightarrow x = 750.$

Hence, Mr. Gautam sold 750 shares.

A man invests ₹ 50,000 of his savings in 12%, ₹ 100 shares at ₹ 125 another ₹ 60,000 in 15%, ₹ 100 shares at ₹ 120 and remainder 18% ₹ 100 shares at ₹ 140. If his annual income is ₹ 21,300 find :

(i) the rate of return on the whole.

(ii) the investment in third company.

Answer

(i) Given,

1st Company = 12%, ₹100 shares at ₹125

Investment = ₹50,000

2nd Company = 15%, ₹100 shares at ₹120

Investment = ₹60,000

3rd Company = 18%, ₹100 shares at ₹ 140

Investment = Remaining

Total annual income = ₹ 21,300

For 1st Company :

Number of shares = $\dfrac{\text{Total investment}}{\text{Market value of each share}} = \dfrac{50000}{125} = 400$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= 400 × $\dfrac{12}{100}$ × 100

= 400 × 12

= ₹ 4,800

For 2nd company :

Number of shares = $\dfrac{\text{Total investment}}{\text{Market value of each share}} = \dfrac{60000}{120} = 500$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= 500 × $\dfrac{15}{100}$ × 100

= 500 × 15

= ₹ 7,500

Income from first two companies = ₹ 4,800 + ₹ 7,500 = ₹ 12,300

Total annual income = ₹ 21,300

Income from 3rd Company = ₹ 21,300 - ₹ 12,300 = ₹ 9,000

Annual income = No. of shares × Rate of div. × N.V. of 1 share

9000 = No. of shares × $\dfrac{18}{100}$ × 100

9000 = No. of shares × 18

No. of shares = $\dfrac{9000}{18}$ = 500

Investment in 3rd company = Number of shares × Market price = 500 × 140 = ₹ 70,000

Total Investment = ₹ 50,000 + ₹ 60,000 + ₹ 70,000 = ₹ 1,80,000

Rate of Return = $\dfrac{\text{Total income}}{\text{Total investment}} \times 100$

= $\dfrac{21300}{180000} \times 100$

= 11.83%

Hence, rate of return = 11.83%.

(ii) Investment in 3rd company = Number of shares × Market price = 500 × 140 = ₹ 70,000

Hence, investment in third company = ₹ 70,000.