Shares & Dividends — Chapter Test

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

Answer

Let the number of shares purchased by the man be x

Nominal Value per share = ₹20

Rate of Dividend = 9%

Annual Dividend = ₹1080

Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share

According to the given,

$1080 = x \times \dfrac{9}{100} \times 20 \\[0.5em] 1080 = \dfrac{9x}{5} \\[0.5em] x = \dfrac{1080 \times 5}{9} \\[0.5em] x = 600$

∴ Number of shares purchased by the man = 600

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

Answer

Nominal Value per share = ₹10

Market Value per share = ₹12

Rate of Dividend = 18%

Dividend on 1 share

$= 18$% $\text{ of ₹10}$

$= \dfrac{18}{100} \times 10 \\[0.5em] = ₹\dfrac{9}{5}$

% $\text{Return} = \Big(\dfrac{\text{Inc. per share}}{\text{M.V. per share}} \times 100\Big)$ %

$= \Big(\dfrac{\frac{9}{5}}{12} \times 100\Big)$ %

$= \Big(\dfrac{9}{5} \times \dfrac{1}{12} \times 100 \Big)$ %

$= \bold{15}$ %

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

(i) the market value of each share.

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

Answer

(i)
Let the market value of each share be ₹x

Total Investment of Mahesh Kulkarni = ₹10000

$\therefore \text{No. of shares} = \dfrac{10000}{x}$

Nominal Value per share = ₹100

Rate of Dividend = 10%

Annual Dividend = ₹800

Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share

According to the given,

$800 = \dfrac{10000}{x} \times \dfrac{10}{100} \times 100 \\[0.5em] 800 = \dfrac{100000}{x} \\[0.5em] x = \dfrac{100000}{800} \\[0.5em] x = 125$

∴ Market Value of each share = ₹125

(ii)

% $\text{Return} = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %

$= \Big(\dfrac{800}{10000} \times 100\Big)$ %

$= \bold{8}$ %

∴ Rate percent Mahesh Kulkarni earns on his investment = 8%

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

Answer

Let the market value of 1 share be ₹x

Dividend on 1 share of ₹100 = 9% of ₹100 = ₹9

% $\text{Return} = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %

As per the given,

$6 = \dfrac{9}{x} \times 100 \\[0.5em] x = \dfrac{9 \times 100}{6} \\[0.5em] x = 150$

∴ 9% ₹100 share should be quoted at ₹150

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

Answer

(i)
Let the number of shares sold by the man be x

Selling price of one share = ₹92
∴ Sales proceeds = ₹92x

Number of ₹100 5% shares purchased by the man

$= \dfrac{92x}{115} \\[0.5em] = \dfrac{4x}{5}$

Annual Income from previous shares = No. of shares x Rate of Dividend x Nominal Value per share

$= x \times \dfrac{2.5}{100} \times 100 \\[0.5em] = \dfrac{25x}{10} \\[0.5em] = \bold{₹\dfrac{5x}{2}}$

Annual Income from new shares = No. of shares x Rate of Dividend x Nominal Value per share

$= \dfrac{4x}{5} \times \dfrac{5}{100} \times 100 \\[0.5em] = \bold{₹4x}$

As per the given,

$4x - \dfrac{5x}{2} = 90 \\[0.5em] \Rightarrow \dfrac{8x - 5x}{2} = 90 \\[0.5em] \Rightarrow \dfrac{3x}{2} = 90 \\[0.5em] \Rightarrow x = \dfrac{90 \times 2}{3} \\[0.5em] \Rightarrow x = 60 \\[0.5em]$

∴ Number of shares sold = 60

(ii)

$\text{No. of shares purchased} = \dfrac{4x}{5} \\[0.5em] = \dfrac{4 \times 60}{5} \\[0.5em] = 48$

∴ Number of shares purchased = 48

(iii)
Annual Income from new shares = ₹4x [From part (i) above]
= ₹(4 x 60)
= ₹240

(iv)
Total Investment = ₹(48 x 115) = ₹5520

% $\text{Return} = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %

$= \Big(\dfrac{240}{5520} \times 100\Big)$ %

$= \Big(\dfrac{2400}{552} \Big)$ %

$= \Big(\dfrac{100}{23} \Big)$ %

$= \bold{4\dfrac{8}{23}}$ %

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

Calculate:

(i) the number of shares before the transaction.

(ii) the number of shares he sold.

(iii) his initial annual income from shares.

Answer

Let the number of 6% ₹100 shares held by the man be x

Number of shares sold by the man = x/2

As the 6% ₹100 shares were at par,
∴ Nominal Value = Market Value = ₹100

As the shares were sold at a discount of 10%,
∴ Selling price of one share = ₹100 - 10% of ₹100 = ₹100 - ₹10 = ₹90

$\therefore \text{Sales proceeds} = 90 \times \dfrac{x}{2} \\[0.5em] = ₹45x$

Market Value of 7% ₹50 shares at a premium of ₹10 = ₹50 + ₹10 = ₹60

Number of 7% ₹50 shares purchased by the man

$= \dfrac{45x}{60} \\[0.5em] = \dfrac{3x}{4}$

Annual Income from previous shares = No. of shares x Rate of Dividend x Nominal Value per share

$= x \times \dfrac{6}{100} \times 100 \\[0.5em] = \bold{₹6x}$

Annual Income from new shares = No. of shares x Rate of Dividend x Nominal Value per share

$= \dfrac{3x}{4} \times \dfrac{7}{100} \times 50 \\[0.5em] = \bold{₹\dfrac{21x}{8}}$

New Annual Income = Annual income from (x/2) 6% ₹100 shares + Annual income from (3x/4) 7% ₹50 shares

$= \dfrac{6x}{2} + \dfrac{21x}{8} \\[0.5em] = 3x + \dfrac{21x}{8} \\[0.5em] = \dfrac{24x + 21x}{8} \\[0.5em] = \dfrac{45x}{8}$

As per the given,

$6x - \dfrac{45x}{8} = 120 \\[0.5em] \Rightarrow \dfrac{48x - 45x}{8} = 120 \\[0.5em] \Rightarrow \dfrac{3x}{8} = 120 \\[0.5em] \Rightarrow x = \dfrac{120 \times 8}{3} \\[0.5em] \Rightarrow x = 320 \\[0.5em]$

(i) Number of shares before the transaction = x = 320

(ii) Number of shares sold = x / 2 = 160

(iii) Initial Income = 6x = 6 x 320 = 1920

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

Answer

Let the investment in 8% ₹100 shares be ₹x, then the investment in 9% ₹50 shares = ₹(101520 - x)

8% ₹100 shares are at 8% discount
∴ Market Value of one 8% ₹100 share = ₹100 - 8% of ₹100 = ₹92

9% ₹50 shares are at 8% premium
∴ Market Value of one 9% ₹50 share = ₹50 + 8% of ₹50 = ₹54

$\text{Income on 1 share of ₹92} = 8$

But the annual incomes from both the investments should be equal

$\therefore \dfrac{2x}{23} = \dfrac{101520 - x}{12} \\[0.5em] \Rightarrow 24x = 2334960 - 23x \\[0.5em] \Rightarrow 47x = 2334960 \\[0.5em] \Rightarrow x = \dfrac{2334960}{47} \\[0.5em] \Rightarrow x = 49680 \\[0.5em] \therefore (101520 -x) = 101520 - 49680 = 51840$

∴ Investment in 8% ₹100 shares at ₹92 = ₹49680
and Investment in 9% ₹50 shares at ₹54 = ₹51840

A man buys ₹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?

Answer

Let the market value of 1 share be ₹x

Dividend on 1 share of ₹40 = 10% of ₹40 = ₹4

$$

As per the given,

$16 = \dfrac{4}{x} \times 100 \\[0.5em] x = \dfrac{4 \times 100}{16} \\[0.5em] x = 25$

∴ The man bought each share at ₹25

A person invested 20%, 30% and 25% of his savings in buying shares at par 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 be ₹4675, find his savings and the amount which he invested in buying shares of each company.

Answer

Let the savings of the person be ₹x.

Amount invested in company A

$= \dfrac{20}{100}x \\[0.5em] = \dfrac{x}{5}$

Amount invested in company B

$= \dfrac{30}{100}x \\[0.5em] = \dfrac{3x}{10}$

Amount invested in company C

$= \dfrac{25}{100}x \\[0.5em] = \dfrac{x}{4}$

As shares are at par so Nominal Value and Market Value of shares are equal.

Dividend from company A

$= \dfrac{10}{100} \times \dfrac{x}{5} \\[0.5em] = \dfrac{x}{50}$

Dividend from company B

$= \dfrac{12}{100} \times \dfrac{3x}{10} \\[0.5em] = \dfrac{9x}{250}$

Dividend from company C

$= \dfrac{15}{100} \times \dfrac{x}{4} \\[0.5em] = \dfrac{3x}{80}$

As per the given,

$\dfrac{x}{50} + \dfrac{9x}{250} + \dfrac{3x}{80} = 4675 \\[0.5em] \Rightarrow \dfrac{40x + 72x + 75x}{2000} = 4675 \\[0.5em] \Rightarrow \dfrac{187x}{2000} = 4675 \\[0.5em] \Rightarrow x = \dfrac{2000 \times 4675}{187}\\[0.5em] \Rightarrow x = 50000 \\[1.5em] \text{Savings of the person} = \bold{₹50000} \\[0.5em] \text{Investment in company A shares} = \dfrac{x}{5} = \dfrac{50000}{5} = \bold{₹10000} \\[0.5em] \text{Investment in company B shares} = \dfrac{3x}{10} = \dfrac{3 \times 50000}{10} = \bold{₹15000} \\[0.5em] \text{Investment in company C shares} = \dfrac{x}{4} = \dfrac{50000}{4} = \bold{₹12500} \\[0.5em]$

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.

Answer

Total Investment of Virat = ₹36000

Nominal Value of Virat's shares = ₹40

As, Virat buys shares at 20% discount, Market Value of Virat's shares

$= ₹40 - 20$

No. of shares purchased by Virat

$= \dfrac{36000}{32} \\[0.5em] = 1125$

Rate of Dividend of Virat's shares = 15%

Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share

Annual Dividend of Virat

$= 1125 \times \dfrac{15}{100} \times 40 \\[0.5em] = ₹6750$

Let rate percent of the dividend declared by Dhoni's company be r%

Total Investment of Dhoni = ₹36000

Nominal Value of Dhoni's shares = ₹75

As, Dhoni buys shares at 20% premium, Market Value of Dhoni's shares

$= ₹75 + 20$

No. of shares purchased by Dhoni

$= \dfrac{36000}{90} \\[0.5em] = 400$

Annual Dividend of Dhoni

$= 400 \times \dfrac{r}{100} \times 75 \\[0.5em] = ₹300r$

As both Dhoni and Virat receive equal dividends,

$\therefore 300r = 6750 \\[0.5em] \Rightarrow r = \dfrac{6750}{300} \\[0.5em] \Rightarrow r = 22.5$

∴ Rate percent of the dividend declared by Dhoni's company = 22.5%

A man invests ₹ 36,000 in 15% ₹ 100 shares at ₹ 120, when the market value of this shares rose to ₹ 200, he sold some shares to purchase a laptop worth ₹ 40,000. Calculate :

(i) the number of shares he still holds

(ii) the dividend he will get on these remaining shares.

Answer

(i) Given,

Investment amount = ₹ 36,000

Face value per share = ₹ 100

Market value per share = ₹ 120

Dividend = 15%

By formula,

Number of shares = $\dfrac{\text{Total investment}}{\text{Market value per share}} = \dfrac{36000}{120}$ = 300

Given,

The man sold some shares to purchase a laptop worth ₹ 40,000, when the shares price rose to ₹ 200. Let no. of shares sold be x.

⇒ x × 200 = 40000

⇒ x = $\dfrac{40000}{200}$ = 200.

Remaining shares = Total shares - sold shares

= 300 - 200 = 100.

Hence, the number of shares he still holds = 100.

(ii) By formula,

Annual dividend = Number of shares x Dividend rate x face value of share

= 100 x $\dfrac{15}{100}$ x 100

= ₹ 1,500

Hence, the dividend the man will get on the remaining shares = ₹ 1,500.