Shares and Dividends

The money required to buy 50, ₹ 20 shares at 10% premium is :

1. ₹ 800

2. ₹ 1,100

3. ₹ 500

4. ₹ 900

Answer

Given,

N.V. of share = ₹ 20

M.V. of share = N.V. + Premium = ₹ 20 + $\dfrac{10}{100} \times 20$ = ₹ 20 + ₹ 2 = ₹ 22.

By formula,

Money required to buy shares = No. of shares × M.V. of each share

= 50 × ₹ 22

= ₹ 1,100.

Hence, Option 2 is the correct option.

The money required to buy 50, ₹ 20 shares at ₹ 10 discount is :

1. ₹ 900

2. ₹ 1,100

3. ₹ 500

4. ₹ 800

Answer

Given,

N.V. of share = ₹ 20

M.V. of share = N.V. - Discount = ₹ 20 - ₹ 10 = ₹ 10.

By formula,

Money required to buy shares = No. of shares × M.V. of each share

= 50 × ₹ 10

= ₹ 500.

Hence, Option 3 is the correct option.

The money required to buy 50, ₹ 20 shares quoted at ₹ 22 is :

1. ₹ 1,100

2. ₹ 2,100

3. ₹ 1,540

4. ₹ 1,440

Answer

Given,

M.V. of share = ₹ 22

By formula,

Money required to buy shares = No. of shares × M.V. of each share

= 50 × ₹ 22

= ₹ 1100.

Hence, Option 1 is the correct option.

₹ 200 shares are available at a discount of 20%. The market price of 50 shares is :

1. ₹ 11,000

2. ₹ 8,000

3. ₹ 19,000

4. ₹ 14,000

Answer

Given,

N.V. of each share = ₹ 200

Discount % = 20%

M.V. of each share = N.V. - Discount = ₹ 200 - $\dfrac{20}{100} \times 200$ = ₹ 200 - ₹ 40 = ₹ 160.

Market price of 50 shares = 50 × Market price of each share

= 50 × ₹ 160

= ₹ 8000.

Hence, Option 2 is the correct option.

500, ₹ 50 shares at par earn a dividend of ₹ 1250 in one year. The rate of dividend is :

1. 10%

2. 7.5%

3. 12.5%

4. 5%

Answer

Given,

N.V. = ₹ 50

No. of shares = 500

Dividend = ₹ 1250

By formula,

Dividend = No. of shares × Rate of dividend × N.V. of share

Let rate of dividend be x%.

Substituting values we get :

$\Rightarrow 1250 = 500 \times x$

Rate of dividend = 5%.

Hence, Option 4 is the correct option.

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

Answer

No. of shares to be bought = 400.

₹ 12.50 shares at a premium of ₹ 1 means; nominal value of the share is ₹ 12.50 and its market value = ₹ 12.50 + ₹ 1 = ₹ 13.50

∴ Money required to buy 400 shares = 400 × ₹ 13.50 = ₹ 5,400.

Hence, money required to buy 400 shares = ₹ 5,400.

How much money will be required to buy 250, ₹ 15 shares at a discount of ₹ 1.50 ?

Answer

No. of shares to be bought = 250.

₹ 15 shares at a discount of ₹ 1.50 means; nominal value of the share is ₹ 15 and its market value = ₹ 15 - ₹ 1.50 = ₹ 13.50

∴ Money required to buy 250 shares = 250 × ₹ 13.50 = ₹ 3,375.

Hence, money required to buy 250 shares = ₹ 3,375.

Find the annual income derived from 125, ₹ 120 shares paying 5% dividend.

Answer

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

= $125 × \dfrac{5}{100} \times 120$

= ₹ 750.

Hence, annual income = ₹ 750.

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

(i) his annual income

(ii) his percentage income on his investment.

Answer

(i) Man invests ₹ 3,072 and M.V. of each share = ₹ 16

No. of shares bought = $\dfrac{3072}{16}$ = 192.

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

= $192 × \dfrac{5}{100} \times 10$

= ₹ 96.

His total annual income = ₹ 96.

(ii) Percentage income = $\dfrac{96}{3072} \times 100 = \dfrac{9600}{3072}$ = 3.125%.

Hence, percentage income = 3.125%.

A man invests ₹ 7,770 in a company paying 5 percent dividend when a share of nominal value of ₹ 100 sells at a premium of ₹ 5. Find :

(i) the number of shares bought;

(ii) annual income;

(iii) percentage income.

Answer

Total money invested = ₹ 7,770

Market value = ₹ 100 + ₹ 5 = ₹ 105

(i) No. of shares bought = $\dfrac{7770}{105}$ = 74.

Hence, no. of shares bought = 74.

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

= $74 × \dfrac{5}{100} \times 100$

= ₹ 370.

His total annual income = ₹ 370.

(iii) Percentage income = $\dfrac{370}{7770} \times 100 = \dfrac{37000}{7770}$ = 4.76%.

Hence, percentage income = 4.76%.

A man buys ₹ 50 shares of a company, paying 12 percent dividend, at a premium of ₹ 10. Find :

(i) the market value of 320 shares;

(ii) his annual income;

(iii) his profit percent.

Answer

(i) Market value of 1 share = ₹ 50 + ₹ 10 = ₹ 60.

∴ Market value of 320 shares = 320 × ₹ 60 = ₹ 19,200.

Hence, market value of 320 shares = ₹ 19,200.

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

= $320 × \dfrac{12}{100} \times 50$

= ₹ 1,920.

His total annual income = ₹ 1,920.

(iii) Profit % = $\dfrac{1920}{19200} \times 100 = \dfrac{192000}{1920}$ = 10%.

Hence, profit % = 10%.

A man invests ₹ 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10 %. If he earns ₹ 1,200 at the end of the year as dividend, find :

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

(ii) the dividend percent per share.

Answer

(i) F.V. = ₹ 100

Premium = 10 % = $\dfrac{10}{100} \times 100$ = ₹ 10.

Market value = ₹ 100 + ₹ 10 = ₹ 110.

Investment = ₹ 8,800

No. of shares = $\dfrac{8800}{110}$ = 80.

Hence, the no. of shares = 80.

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

Let dividend percent = x%,

1200 = $80 × \dfrac{x}{100} \times 100$

1200 = 80x

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

Hence, dividend percent per share = 15%.

A man invests ₹ 1,680 in buying shares of nominal value ₹ 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate:

(i) the number of shares he buys;

(ii) the dividend he receives annually.

Answer

(i) F.V. = ₹ 24

Premium = 12 % = $\dfrac{12}{100} \times 24$ = ₹ 2.88.

Market value = ₹ 24 + ₹ 2.88 = ₹ 26.88.

Investment = ₹ 1,680

No. of shares = $\dfrac{1680}{26.88}$ = 62.5.

Hence, the no. of shares = 62.5.

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

= $62.5 × \dfrac{15}{100} \times 24$

= 225.

Hence, dividend received annually = ₹ 225.

By investing ₹ 7,500 in a company paying 10 percent dividend, an annual income of ₹ 500 is received. What price is paid for each of ₹ 100 share ?

Answer

Let x be price paid for each share.

No. of shares = $\dfrac{7500}{x}$

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

$\Rightarrow 500 = \dfrac{7500}{x} × \dfrac{10}{100} \times 100 \\[1em] \Rightarrow x = \dfrac{75000}{500} = 150.$

Hence, price paid for ₹ 100 share = ₹ 150.

The number of ₹ 25 shares, paying 24% dividend, with total dividend ₹ 1,350 is :

1. 125

2. 27

3. 225

4. 200

Answer

Given,

Dividend = ₹ 1350

N.V. of share = ₹ 25

Rate of dividend = 24%

Let no. of shares be n.

By formula,

Dividend = No. of shares × Rate of dividend × N.V. of share

Substituting values we get :

$\Rightarrow 1350 = n \times 24$

Hence, Option 3 is the correct option.

₹ 600 shares of a company are available at a discount of 20%. If the company pays a dividend of 20%, the rate of return is :

1. 16%

2. 25%

3. 10%

4. 12.5%

Answer

Given,

N.V. of share = ₹ 600

Discount = 20%

M.V. = N.V. - Discount

= ₹ 600 - 20%

= ₹ 600 - $\dfrac{20}{100} \times 600$

= ₹ 600 - ₹ 120 = ₹ 480.

Dividend = 20%

Let rate of return be r%.

We know that,

Interest on M.V. = Dividend on N.V.

r% of ₹ 480 = 20% of ₹ 600

$\Rightarrow \dfrac{r}{100} \times 480 = \dfrac{20}{100} \times 600 \\[1em] \Rightarrow 4.8r = 120 \\[1em] \Rightarrow r = \dfrac{120}{4.8} \\[1em] \Rightarrow r = 25$

Hence, Option 2 is the correct option.

Rajesh invested ₹ 75,000 in a company paying 10% dividend. If ₹ 10 shares of this company are available for ₹ 15, the return on these shares is :

1. ₹ 2,500

2. ₹ 5,000

3. ₹ 3,750

4. ₹ 7,500

Answer

No. of shares bought = $\dfrac{\text{Sum deposited}}{\text{M.V. of each share}} = \dfrac{75000}{15}$ = 5000.

Dividend on 1 share = Dividend % × N.V. of each share

= $\dfrac{10}{100} \times 10$ = ₹ 1.

Dividend on 5000 shares = 5000 × ₹ 1 = ₹ 5000.

Hence, Option 2 is the correct option.

100 shares at par value of ₹ 120 each, give 10% half-yearly dividend. The annual dividend from these shares is :

1. ₹ 7200

2. ₹ 2400

3. ₹ 1200

4. ₹ 10800

Answer

Given,

Dividend % = 10% half-yearly or 20% yearly.

N.V. = ₹ 120

No. of shares = 100

By formula,

Dividend = No. of shares × Rate of dividend × N.V. of share

Substituting values we get :

$\text{Dividend} = 100 \times 20$

Hence, Option 2 is the correct option.

200 ₹ 20 shares, each available at a discount of 20%, give 10% dividend. The rate of return is :

1. 12.5%

2. 15%

3. 16%

4. 25%

Answer

Given,

Dividend = 10%

N.V. = ₹ 20

Discount = 20%

M.V. = N.V. - Discount

= ₹ 20 - 20%

= ₹ 20 - $\dfrac{20}{100} \times 20$

= ₹ 20 - ₹ 4 = ₹ 16.

Dividend = 10%

Let rate of return/interest be r%.

We know that,

Interest on M.V. = Dividend on N.V.

r% of 16 = 10% of 20

$\Rightarrow \dfrac{r}{100} \times 16 = \dfrac{10}{100} \times 20 \\[1em] \Rightarrow r = \dfrac{10 \times 20}{16} \\[1em] \Rightarrow r = \dfrac{200}{16} \\[1em] \Rightarrow r = 12.5$

Hence, Option 1 is the correct option.

A man buys 75, ₹ 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?

Answer

We know that,

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

Let M.V. of each share be x.

$\Rightarrow \dfrac{9}{100} \times 100 = \dfrac{12}{100} \times x \\[1em] \Rightarrow x = \dfrac{9 \times 100}{12} \\[1em] \Rightarrow x = 75.$

Hence, cost of share is ₹ 75 each.

By purchasing ₹ 25 gas shares for ₹ 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?

Answer

Profit = 4% = $\dfrac{4}{100} \times 40 = 1.6$

Let company be paying x% dividend.

As,

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

⇒ 1.6 = 1 × $\dfrac{x}{100}$ × 25

⇒ x = $\dfrac{160}{25}$ = 6.4%.

For 60 shares dividend = 60 $\times \dfrac{6.4}{100} \times 25$ = ₹ 96.

Hence, rate paid by company = 6.4% and dividend = ₹ 96.

Hundred rupee shares of a company are available in the market at a premium of ₹ 20. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.

Answer

We know that,

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

Market value = ₹ 100 + ₹ 20 = ₹ 120.

Let rate of dividend be x%

$\Rightarrow \dfrac{x}{100} \times 100 = \dfrac{15}{100} \times 120 \\[1em] \Rightarrow x = 18$

Hence, rate of dividend = 18%.

₹ 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.

Answer

We know that,

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

Market value = ₹ 50 - ₹ $\dfrac{10}{100} \times 50$ = ₹ 50 - ₹ 5 = ₹ 45.

Let rate of dividend be x%

$\Rightarrow \dfrac{x}{100} \times 50 = \dfrac{20}{100} \times 45 \\[1em] \Rightarrow x = \dfrac{20 \times 45}{50} \\[1em] \Rightarrow x = 18$

Hence, rate of dividend = 18%.

A company declares 8 percent dividend to the share holders. If a man receives ₹ 2,840 as his dividend, find the nominal value of his shares.

Answer

Let nominal value of share be ₹ x

Given, dividend% = 8% and dividend = ₹ 2,840

$\therefore \dfrac{8}{100} \times x = 2840 \\[1em] \Rightarrow x = \dfrac{2840 \times 100}{8} \\[1em] \Rightarrow x = 35,500.$

Hence, nominal value of shares = ₹ 35,500.

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

Answer

Let man invest ₹ x

∴ No. of shares = $\dfrac{x}{110}$

We know that,

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

$\Rightarrow 1680 = \dfrac{x}{110} \times \dfrac{12}{100} \times 100 \\[1em] \Rightarrow x = \dfrac{1680 \times 110}{12} \\[1em] \Rightarrow x = 15,400$

Hence, investment = ₹ 15,400.

A company declares a dividend of 11.2% to all its share-holders. If its ₹ 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 ₹ 1,680?

Answer

Let man invest ₹ x

Market value = ₹ 60 + $\dfrac{25}{100} \times 60$ = ₹ 60 + ₹ 15 = ₹ 75

∴ No. of shares = $\dfrac{x}{75}$

We know that,

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

$\Rightarrow 1680 = \dfrac{x}{75} \times \dfrac{11.2}{100} \times 60 \\[1em] \Rightarrow x = \dfrac{1680 \times 100 \times 75}{11.2 \times 60} \\[1em] \Rightarrow x = 18,750$

Hence, investment = ₹ 18,750.

A man buys 400, twenty-rupee shares at a premium of ₹ 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.

Answer

(i) Market value = ₹ 20 + ₹ 4 = ₹ 24.

Amount invested = 400 × ₹ 24 = ₹ 9,600

Hence, amount invested = ₹ 9,600.

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

= 400 × $\dfrac{12}{100} \times 20$

= ₹ 960.

Hence, annual income = ₹ 960.

(iii) Percentage return = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{960}{9600} \times 100$ = 10%.

Hence, percentage return = 10%.

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.

Answer

(i) Market value = ₹ 20 - ₹ $\dfrac{20}{100} \times 20$ = ₹ 20 - ₹ 4 = ₹ 16.

Amount invested = 400 × ₹ 16 = ₹ 6,400

Hence, amount invested = ₹ 6,400.

(ii) Let rate of dividend be x%.

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

$\Rightarrow \dfrac{x}{100} \times 20 = \dfrac{12}{100} \times 16 \\[1em] \Rightarrow x = \dfrac{12 \times 16}{20} \\[1em] \Rightarrow x = \dfrac{48}{5} = 9.6$

Hence, rate of dividend = 9.6%.

A company with 10,000 shares of ₹ 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.

Answer

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

= 10,000 × $\dfrac{5}{100} \times 100$

= ₹ 50,000.

Hence, total dividend = ₹ 50,000.

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

= 72 × $\dfrac{5}{100} \times 100$

= ₹ 360.

Hence, annual income of man = ₹ 360.

(iii) Let investment be ₹ x.

Given return % = 4%.

$\therefore 4 = \dfrac{360}{x} \times 100 \\[1em] \Rightarrow x = \dfrac{36000}{4} = 9,000.$

Price paid for each share = $\dfrac{\text{Investment}}{\text{No. of shares}} = \dfrac{9000}{72} = 125.$

Hence, price of each share = ₹ 125.

A lady holds 1800, ₹ 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what is the return she gets as percent on her investment?

Give your answer to nearest integer.

Answer

Market value = ₹ 100 + ₹ $\dfrac{40}{100} \times 100$ = ₹ 100 + ₹ 40 = ₹ 140.

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

= 1800 × $\dfrac{15}{100} \times 100$

= ₹ 27,000.

Investment = No. of shares × M.V. = 1800 × ₹ 140 = ₹ 2,52,000.

Return % = $\dfrac{\text{Dividend}}{\text{Investment}} \times 100 = \dfrac{27000}{252000} \times 100 =$ 10.71% ≈ 11%.

Hence, annual dividend = ₹ 27,000 and return % = 11%.

A man invests ₹ 11,200 in a company paying 6 percent per annum when its ₹ 100 shares can be bought for ₹ 140. Find :

(i) his annual dividend

(ii) his percentage return on his investment.

Answer

(i) Market value = ₹ 140

Investment = ₹ 11,200

No. of shares = $\dfrac{\text{Investment}}{\text{M.V.}} = \dfrac{11200}{140} = 80.$

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

= 80 × $\dfrac{6}{100} \times 100$

= ₹ 480.

Hence, annual dividend = ₹ 480.

(ii) Return% = $\dfrac{\text{Annual dividend}}{\text{Investment}} \times 100 = \dfrac{480}{11200} \times 100$ = 4.29%

Hence, return % = 4.29%.

Mr. Sharma has 60 shares of N.V. ₹ 100 and sells them when they are at a premium of 60%. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4% discount, and paying 18% dividend annually. Calculate :

(i) the sale proceeds

(ii) the number of shares he buys; and

(iii) his annual dividend from the shares.

Answer

(i) Market value of initial shares = ₹ 100 + $\dfrac{60}{100} \times 100$ = ₹ 100 + ₹ 60 = ₹ 160.

Sale proceeds = 60 × ₹ 160 = ₹ 9,600.

Hence, sale proceeds = ₹ 9,600.

(ii) M.V. of second shares = ₹ 50 - $\dfrac{4}{100} \times 50$ = ₹ 50 - ₹ 2 = ₹ 48.

No. of shares = $\dfrac{9600}{48}$ = 200.

Hence, no. of shares = 200.

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

= 200 × $\dfrac{18}{100} \times 50$

= ₹ 1,800.

Hence, annual dividend = ₹ 1,800.

A company with 10,000 shares of nominal value ₹ 100 declares an annual dividend of 8% to the share-holders.

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

(ii) Ramesh had bought 90 shares of the company at ₹ 150 per share. Calculate dividend he receives and percentage return on his investment.

Answer

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

= 10,000 × $\dfrac{8}{100} \times 100$

= ₹ 80,000.

Hence, annual dividend paid by company = ₹ 80,000.

(ii) Investment = 90 × ₹ 150 = ₹ 12,500

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

= 90 × $\dfrac{8}{100} \times 100$

= ₹ 720.

Return% = $\dfrac{\text{Annual dividend}}{\text{Investment}} \times 100 = \dfrac{720}{12500} \times 100 = 5\dfrac{1}{3}$%

Hence, dividend received by Ramesh = ₹ 720 and return % = $5\dfrac{1}{3}$%.

Which is better investment : 16% of ₹ 100 shares at 80 or 20% ₹ 100 shares at 120?

Answer

Since, Profit% on M.V. = Dividend% on N.V.

In first case :

P% on ₹ 80 = 16% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 80 = \dfrac{16}{100} \times 100 \\[1em] \Rightarrow P = \dfrac{16}{80} \times 100 = 20$

In second case :

P% on ₹ 120 = 20% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 120 = \dfrac{20}{100} \times 100 \\[1em] \Rightarrow P = \dfrac{20}{120} \times 100 = 16\dfrac{4}{6}$

Hence, 16% of ₹ 100 shares at 80 is the better investment.

A man has a choice to invest in hundred-rupee shares of two firms at ₹ 120 or at ₹ 132. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum. Find :

(i) which company is giving a better return.

(ii) if a man invests ₹26,400 with each firm, how much will be the difference between the annual returns from the two firms ?

Answer

(i) First company's dividend = 5% and second company's = 6%.

∴ Second company is giving a better return.

(ii) No. of shares of first company = $\dfrac{26400}{120} = 220$

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

= 220 × $\dfrac{5}{100} \times 100$

= ₹ 1,100.

No. of shares of second company = $\dfrac{26400}{132} = 200$

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

= 200 × $\dfrac{6}{100} \times 100$

= ₹ 1,200.

Difference between annual returns = ₹ 1200 - ₹ 1100 = ₹ 100.

Hence, difference between annual returns of two firms = ₹ 100.

A man bought 360, ten-rupee shares of a company, paying 12 percent per annum. He sold shares when their price rose to ₹ 21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at ₹ 3.50 per share. Find annual change in his income.

Answer

In first case :

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

= 360 × $\dfrac{12}{100} \times 10$

= ₹ 432

S.P. of shares = 360 × ₹ 21 = ₹ 7,560

M.V. of second shares = ₹ 3.50

No. of shares purchased = $\dfrac{\text{Investment}}{\text{M.V. of share}} = \dfrac{7560}{3.5}$ = 2160.

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

= 2160 × $\dfrac{4.5}{100} \times 5$

= ₹ 486.

Change in income = ₹ 486 - ₹ 432 = ₹ 54.

Hence, the change in income = ₹ 54 (increase).

A man sold 400 (₹ 20) shares of a company, paying 5% at ₹ 18 and invested the proceeds in (₹ 10) shares of another company paying 7% at ₹ 12. How many (₹ 10) shares did he buy and what was the change in his income ?

Answer

In first case :

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

= 400 × $\dfrac{5}{100} \times 20$

= ₹ 400.

S.P. of shares = 400 × ₹ 18 = ₹ 7,200

M.V. of second type of shares = ₹ 12

No. of shares purchased = $\dfrac{\text{Investment}}{\text{M.V. of share}} = \dfrac{7200}{12}$ = 600.

In second case :

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

= 600 × $\dfrac{7}{100} \times 10$

= ₹ 420.

Change in income = ₹ 420 - ₹ 400 = ₹ 20.

Hence, no. of shares (₹ 10) bought = 600 and change in income = ₹ 20 (increase).

Two brothers A and B invest ₹ 16,000 each in buying shares of two companies. A buys 3% hundred rupee shares at 80 and B buys ten-rupee shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B.

Answer

For A,

M.V. of shares = 80

Investment = ₹ 16,000

No. of shares = $\dfrac{16000}{80}$ = 200.

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

= 200 × $\dfrac{3}{100} \times 100$

= ₹ 600.

For B,

M.V. of shares = 10

Investment = ₹ 16,000

No. of shares = $\dfrac{16000}{10}$ = 1600.

Let rate of dividend be x%

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

$\Rightarrow 600 = 1600 \times \dfrac{x}{100} \times 10 \\[1em] \Rightarrow x = \dfrac{600 \times 100}{1600 \times 10} \\[1em] \Rightarrow x = \dfrac{60000}{16000} = 3.75$

Hence, the rate percent of the dividend received by B = 3.75%.

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.

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 = $\dfrac{45500}{x}$

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.

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

(i) the number of shares he bought.

(ii) his total investment.

(iii) the rate of return on his investment.

Answer

(i) Let no. of shares be x.

Annual income = 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 = 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%.

How much should a man invest in ₹ 50 shares selling at ₹ 60 to obtain an income of ₹ 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.

Answer

Let investment = ₹ x.

M.V. = ₹ 60

No. of shares = $\dfrac{x}{60}$

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

450 = $\dfrac{x}{60} \times \dfrac{10}{100} \times 50$

x = 450 × 12 = 5,400

Yield % = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{450}{5400} \times 100$ = 8.33% ≈ 8%.

Hence, investment = ₹ 5,400 and yield % = 8%.