Shares & Dividends — Exercise 3

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

Answer

Dividend on 1 share

$= 9$

∴ Dividend on 60 shares
= ₹1.8 * 60
= ₹108

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

Hint — Let the nominal value of his shares be ₹x, then 8% of ₹x = ₹2840.

Answer

Let nominal value of shares be ₹x

According to the given,

$8$

∴ Nominal value of the man's shares = ₹35500

A man buys 250, ten-rupee shares each at ₹12.50. If the rate of dividend is 7%, find the :

(a) dividend he receives annually.

(b) percentage return on his investment.

Answer

(a) Nominal Value of 1 share = ₹10

Market Value of 1 share = ₹12.50

Number of shares purchased = 250

Nominal Value of 250 shares = 250 x 10 = ₹2500

Rate of dividend = 7%

∴ Dividend received = 7% of 2500

= $\dfrac{7}{100} \times 2500$

= ₹175.

Hence, annual dividend = ₹175.

(b) Amount Invested = No. of shares x Market Value

= 250 x 12.50

= ₹3125

$\text{Return percentage } = \dfrac{\text{Dividend received}}{\text{Investment}} \times 100 \\[1em] = \dfrac{175}{3125} \times 100 \\[1em] = \dfrac{17500}{3125} \\[1em] = 5.6$

Hence, return percentage = 5.6%.

Find the market price of 5% ₹100 share when a person gets a dividend of ₹65 by investing ₹1430.

Answer

Let the number of shares purchased be x

Nominal Value per share = ₹100

Rate of Dividend = 5%

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

According to the given,

$65 = x \times \dfrac{5}{100} \times 100 \\[0.5em] 65 = 5x \\[0.5em] x = \dfrac{65}{5} \\[0.5em] x = 13$

∴ No. of shares purchased = 13

Total Investment = ₹1430

∴ Market Price of one share

$= \dfrac{\text{Total Investment}}{\text{No. of shares}} \\[0.7em] = \dfrac{1430}{13} \\[0.5em] = \bold{₹110}$

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

(i) What is his investment?

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

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

Answer

Number of shares = 50

Face value per share = ₹100

Market value per share = ₹132

(i)
Total Investment = No. of shares x Market value per share

$= 50 \times 132 \\ = 6600$

∴ Govind investment = ₹6600

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

$= 50 \times \dfrac{7.5}{100} \times 100 \\[0.5em] = 375$

∴ Govind Annual Income = ₹375

(iii)
Increase in Annual Income = ₹150

New Annual Income = ₹375 + ₹150 = ₹525

Let the new number of shares by x

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

According to the given,

$525 = x \times \dfrac{7.5}{100} \times 100 \\[0.5em] 525 = 7.5x \\[0.5em] x = \dfrac{5250}{75} \\[0.5em] x = 70$

∴ New number of shares = 70

Extra shares Govind should buy
= 70 - 50
= 20

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 percentage return does she get on her investment?

Answer

No. of shares held = 1800

Nominal Value per share = ₹100

Rate of Dividend = 15%

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

$= 1800 \times \dfrac{15}{100} \times 100 \\[0.5em] = 27000$

∴ Annual Dividend = ₹27000

As Shares are bought at 40% premium,

Market Value of one share

$= 100 + \Big(\dfrac{40}{100} \times 100\Big) \\[0.5em] = 100 + 40 \\[0.5em] = ₹140$

Total Investment = No. of shares x Market Value per share
= 1800 x 140
= ₹252000

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

$= \Big(\dfrac{27000}{252000} \times 100\Big)$ %

$= \Big(\dfrac{2700}{252} \Big)$ %

$= \Big(\dfrac{75}{7} \Big)$ %

$= \bold{10\frac{5}{7}}$ %

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

Answer

Let the number of shares purchased be x.

Nominal Value per share = ₹25

Market Value per share = ₹36

Rate of Dividend = 12%

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

According to the given,

$720 = x \times \dfrac{12}{100} \times 25 \\[0.5em] 720 = 3x \\[0.5em] x = \dfrac{720}{3} \\[0.5em] x = 240$

∴ Total Investment Required = No. of shares x Market Value per share
= 240 x 36
= ₹8640

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

$= \Big(\dfrac{720}{8640} \times 100\Big)$ %

$= \Big(\dfrac{72000}{8640} \Big)$ %

$= \Big(\dfrac{25}{3} \Big)$ %

$= \bold{8\frac{1}{3}}$ %

Ashok invests ₹26400 on 12% ₹25 shares of a company. If he receives a dividend of ₹2475, find:

(i) the number of shares he bought.
(ii) the market value of each share.

Answer

Let the number of shares purchased be x.

Nominal Value per share = ₹25

Rate of Dividend = 12%

Total Investment = ₹26400

Annual Dividend = ₹2475

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

According to the given,

$2475 = x \times \dfrac{12}{100} \times 25 \\[0.5em] 2475 = 3x \\[0.5em] x = \dfrac{2475}{3} \\[0.5em] x = 825$

∴ Number of shares bought = 825

Market value of each share

$= \dfrac{\text{Total Investment}}{\text{No. of shares}} \\[0.7em] = \dfrac{26400}{825} \\[0.5em] = \bold{₹32}$

A man invests ₹4500 in shares of a company which is paying 7.5% dividend. If ₹100 shares are available at a discount of 10%, find

(i) the number of shares he purchases.

(ii) his annual income.

Answer

Nominal Value per share = ₹100

Rate of Dividend = 7.5%

Total Investment = ₹4500

As the shares are bought at a discount of 10%,

Market Value per share = ₹100 - ₹(10% of 100)

$= ₹100 - ₹\Big(\dfrac{10}{100} \times 100 \Big) \\[0.5em] = ₹100 - ₹10 \\[0.5em] = ₹90$

(i) Number of shares purchased

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{4500}{90} \\[0.5em] = \bold{50}$

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

$= 50 \times \dfrac{7.5}{100} \times 100 \\[0.5em] = \bold{₹375}$

Hence, his annual income = ₹375

Amit invests ₹36000 in buying ₹100 shares at ₹20 premium. The dividend is 15% per annum. Find:

(i) the number of shares he buys

(ii) his yearly dividend

(iii) the percentage return on his investment.

Answer

Nominal Value per share = ₹100

Rate of Dividend = 15%

Total Investment = ₹36000

As Amit buys the shares at ₹20 premium,

Market Value per share = ₹100 + ₹20 = ₹120

∴ Number of shares he buys

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{36000}{120} \\[0.5em] = \bold{300}$

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

$= 300 \times \dfrac{15}{100} \times 100 \\[0.5em] = \bold{₹4500}$

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

$= \Big(\dfrac{4500}{36000} \times 100\Big)$ %

$= \Big(\dfrac{450000}{36000} \Big)$ %

$= \Big(\dfrac{25}{2} \Big)$ %

$= \bold{12.5}$ %

Mr. Gupta invested ₹33000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%.

Find:

(a) the number of shares purchased by him.

(b) his annual dividend.

Answer

Money invested = ₹33000

N.V. of share = ₹100

M.V. = N.V + Premium

= ₹100 + $\dfrac{10}{100} \times 100$

= ₹100 + ₹10

= ₹110.

(a) Number of shares = $\dfrac{\text{Money invested}}{\text{M.V.}} = \dfrac{33000}{110}$ = 300.

Hence, no. of shares purchased = 300.

(b) By formula,

Annual dividend = Number of shares × Rate of dividend × N.V.

= 300 × $\dfrac{12}{100} \times 100$

= ₹3600.

Hence, annual dividend = ₹3600.

A man buys shares at the par value of ₹10 yielding 8% dividend at the end of a year. Find the number of shares bought if he receives a dividend of ₹300.

Answer

As shares are bought at par,
Market value per share = Nominal value per share = ₹10

Rate of Dividend = 8%

Annual Dividend = ₹300

Let the number of shares purchased be x.

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

According to the given,

$300 = x \times \dfrac{8}{100} \times 10 \\[0.5em] x = \dfrac{300 \times 10}{8} \\[0.5em] x = 375$

∴ Number of shares bought = 375

A man invests ₹8800 on buying shares of face value of rupees hundred each at a premium of 10%. If he earns ₹1200 at the end of year as dividend, find:

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

(ii) the dividend percentage per share.

Answer

Nominal Value per share = ₹100

Total Investment = ₹8800

Annual Dividend = ₹1200

(i)
As the shares were bought at 10% premium,

Market Value of one share

$= 100 + \Big(\dfrac{10}{100} \times 100\Big) \\[0.5em] = 100 + 10 \\[0.5em] = ₹110$

Number of shares bought

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{8800}{110} \\[0.5em] = \bold{80}$

∴ Number of shares the man has in the company = 80

(ii)
Let the dividend percentage per share be r%

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

According to the given,

$1200 = 80 \times \dfrac{r}{100} \times 100 \\[0.5em] 1200 = 80r \\[0.5em] r = \dfrac{1200}{80} \\[0.5em] r = 15$

∴ Dividend percentage per share = 15%

A man invested ₹45000 in 15% ₹100 shares quoted at ₹125. When the market value of these shares rose to ₹140, he sold some shares, just enough to raise ₹8400. Calculate:

(i) The number of shares he still holds.

(ii) The dividend due to him on these shares.

Answer

(i)
Nominal Value per share = ₹100

Market Value per share = ₹125

Total Investment = ₹45000

Rate of Dividend = 15%

No. of shares bought at MV of ₹125

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.5em] = \dfrac{45000}{125} \\[0.5em] = 360$

∴ Total number of shares = 360

Market Value per share of shares sold = ₹140

Amount raised from sale = ₹8400

$\text{No. of shares sold} \\[0.5em] = \dfrac{\text{Amt raised from sale}}{\text{MV per share}} \\[0.5em] = \dfrac{8400}{140} \\[0.5em] = 60$

No. of shares remaining = Total shares - Shares sold
= 360 - 60
= 300

∴ Number of shares the man still holds = 300

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

$= 300 \times \dfrac{15}{100} \times 100 \\[0.5em] = \bold{₹4500}$

∴ Dividend due to the man on remaining shares = ₹4500

Ajay owns 560 shares of a company. The face value of each share is ₹25. The company declares a dividend 0f 9%. Calculate:

(i) the dividend that Ajay will get

(ii) the rate of interest, on his investment, if Ajay has paid ₹30 for each share.

Answer

Nominal Value per share = ₹25

Rate of Dividend = 9%

No. of shares owned = 560

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

$= 560 \times \dfrac{9}{100} \times 25 \\[0.5em] = ₹1260$

∴ The dividend that Ajay will get = ₹1260

(ii)
Market Value per share = ₹30

Total Investment = No. of shares x Market Value per share
= 560 x 30
= 16800

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

$= \Big(\dfrac{1260}{16800} \times 100\Big)$ %

$= \Big(\dfrac{1260}{168} \Big)$ %

$= \Big(\dfrac{15}{2} \Big)$ %

$= \bold{7\frac{1}{2}}$ %

∴ Rate of return on Ajay's investment = 7½%

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

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

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

Answer

(i)
No. of shares = 10000

Nominal Value per share = ₹100

Rate of Dividend = 8%

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

$= 10000 \times \dfrac{8}{100} \times 100 \\[0.5em] = ₹80000$

∴ Total amount of dividend paid by the company = ₹80000

(ii)
No. of shares Ramesh bought = 90

Nominal Value per share = ₹100

Rate of Dividend = 8%

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

$= 90 \times \dfrac{8}{100} \times 100 \\[0.5em] = ₹720$

∴ Dividend Ramesh received = ₹720

Total investment of Ramesh = 90 x 150 = ₹13500

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

$= \Big(\dfrac{720}{13500} \times 100\Big)$ %

$= \Big(\dfrac{720}{135} \Big)$ %

$= \Big(\dfrac{16}{3} \Big)$ %

$= \bold{5\frac{1}{3}}$ %

A company with 500 shares of nominal value ₹ 120 declares and annual dividend of 15%. Calculate :

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

(ii) the annual income of Mr Sharma who hold 80 shares of the company.

If the return percent of Mr. Sharma from his shares is 10%, find the market value of each shares.

Answer

(i) No. of shares = 500

Nominal Value per share = ₹ 120

Rate of Dividend = 15%

By formula,

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

= 500 x $\dfrac{15}{100}$ x 120

= ₹ 9,000

Hence, total amount of dividend paid by the company = ₹ 9,000.

(ii) No. of shares held by Mr. Sharma = 80

Nominal Value per share = ₹ 120

Rate of Dividend = 15%

By formula,

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

= 80 x $\dfrac{15}{100}$ x 120

= ₹ 1,440.

Hence, annual income of Mr. Sharma = ₹ 1,440.

By formula,

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

$\Rightarrow \dfrac{15}{100} \times 120 = \dfrac{10}{100} \times M.V. \\[1em] \Rightarrow 15 \times 120 = 10 \times M.V. \\[1em] \Rightarrow M.V. = \dfrac{15 \times 120}{10} = 180.$

Hence, market value of each share = ₹ 180.

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

Answer

Let the number of shares purchased be x.

Nominal Value per share = ₹100

Rate of Dividend = 10%

Total Investment = ₹7500

Annual Dividend = ₹500

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

According to the given,

$500 = x \times \dfrac{10}{100} \times 100 \\[0.5em] 500 = 10x \\[0.5em] x = \dfrac{500}{10} \\[0.5em] x = 50$

∴ Number of shares purchased = 50

Market value of each share

$= \dfrac{\text{Total Investment}}{\text{No. of shares}} \\[0.7em] = \dfrac{7500}{50} \\[0.5em] = \bold{₹150}$

∴ Price paid for each share = ₹150

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

(i) his investment

(ii) dividend received

(iii) yield.

Answer

(i)
Number of shares = 400

Nominal Value per share = ₹10

As the man buys the shares at ₹2.50 premium,

Market Value per share = ₹10 + ₹2.50 = ₹12.50

Total Investment = No. of shares x MV per share
= 400 x 12.5
= 5000

∴ Investment of man = ₹5000

(ii)
Rate of Dividend = 8%

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

$= 400 \times \dfrac{8}{100} \times 10 \\[0.5em] = \bold{₹320}$

∴ Dividend received = ₹320

(iii)
Yield means the rate of return on investment.

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

$= \Big(\dfrac{320}{5000} \times 100\Big)$ %

$= \Big(\dfrac{32}{5} \Big)$ %

$= \bold{6.4}$ %

∴ Yield = 6.4%

A man invests ₹10400 in 6% shares at ₹104 and ₹11440 in 10.4% shares at ₹143. How much income would he get in all? (Assume face value of ₹100)

Answer

First Investment:

Total Investment = ₹10400

Market Value per share = ₹104

∴ No. of shares

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{10400}{104} \\[0.5em] = \bold{100}$

Rate of Dividend = 6%

As Nominal value is not given, let's assume it to be ₹100 per share

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

$= 100 \times \dfrac{6}{100} \times 100 \\[0.5em] = \bold{₹600}$

Second Investment:

Total Investment = ₹11440

Market Value per share = ₹143

∴ No. of shares

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{11440}{143} \\[0.5em] = \bold{80}$

Rate of Dividend = 10.4%

As Nominal value is not given, let's assume it to be ₹100 per share

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

$= 80 \times \dfrac{10.4}{100} \times 100 \\[0.5em] = \bold{₹832}$

Total Income = Income from first investment + Income from second investment
= ₹600 + ₹832
= ₹1432

∴ Total Income = ₹1432

Two companies have shares of 7% at ₹116 and 9% at ₹145 respectively. In which of the shares would the investment be more profitable?(Assume face value of ₹100)

Answer

Assuming nominal value per share to be ₹100 in both cases.

In the first case:

Income on ₹116 = 7% of ₹100 = ₹7

$\therefore \text{ Income on ₹1} = ₹\dfrac{7}{116}$

In the second case:

Income on ₹145 = 9% of ₹100 = ₹9

$\therefore \text{ Income on ₹1} = ₹\dfrac{9}{145}$

Now,

$\dfrac{7}{116} = \dfrac{7 \times 5}{116 \times 5} = \dfrac{35}{580} \\[0.7em] \dfrac{9}{145} = \dfrac{9 \times 4}{145 \times 4} = \dfrac{36}{580}$

Since 35 < 36, therefore investment in second case (i.e. 9% at ₹145) is more profitable than the investment in first case.

Which is better investment : 6% ₹100 shares at ₹120 or 8% ₹10 shares at ₹15

Answer

In the first case:

Income on ₹120 = 6% of ₹100 = ₹6

$\therefore \text{ Income on ₹1} = ₹\dfrac{6}{120} \\[0.5em] = ₹\dfrac{1}{20}$

In the second case:

Income on ₹15 = 8% of ₹10 = ₹0.8

$\therefore \text{ Income on ₹1} = ₹\dfrac{0.8}{15} \\[0.5em] = ₹\dfrac{8}{150} \\[0.5em] = ₹\dfrac{4}{75}$

Now,

$\dfrac{1}{20} = \dfrac{1 \times 15}{20 \times 15} = \dfrac{15}{300} \\[0.7em] \dfrac{4}{75} = \dfrac{4 \times 4}{75 \times 4} = \dfrac{16}{300}$

Since 15 < 16, therefore investment in second case (i.e. 8% ₹10 shares at ₹15) is more profitable than the investment in first case.

A man invests ₹10080 in 6% hundred-rupee shares at ₹112. Find his annual income. When the shares fall to ₹96 he sells out the shares and invests the proceeds in 10% ten-rupee shares at ₹8. Find the change in his annual income.

Answer

Total Investment = ₹10080

Market Value per share = ₹112

∴ No. of shares

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{10080}{112} \\[0.5em] = \bold{90}$

Rate of Dividend = 6%

Nominal value per share = ₹100

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

$= 90 \times \dfrac{6}{100} \times 100 \\[0.5em] = \bold{₹540}$

∴ Annual Income = ₹540

Let's calculate the Annual Income of his new investment.

Selling price of 1 share = ₹96
∴ Selling price of 90 shares = ₹(90 x 96) = ₹8640

Hence, sale proceeds = ₹8640

Total Investment in new shares = ₹8640

Market Value per share of new shares = ₹8

∴ No. of new shares

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{8640}{8} \\[0.5em] = \bold{1080}$

Nominal value per share of new shares = ₹10

Rate of Dividend of new shares = 10%

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

$= 1080 \times \dfrac{10}{100} \times 10 \\[0.5em] = \bold{₹1080}$

∴ Change in Annual Income = ₹1080 - ₹540 = ₹540

Annual Income increased by ₹540

Sachin invests ₹8500 in 10% ₹100 shares at ₹170. He sells the shares when the price of each share rises by ₹30. He invests the proceeds in 12% ₹100 shares at ₹125. Find

(i) the sale proceeds.

(ii) the number of ₹125 shares he buys.

(iii) the change in his annual income.

Answer

(i) Total Investment = ₹8500

Market Value per share = ₹170

∴ No. of shares

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{8500}{170} \\[0.5em] = \bold{50}$

Selling price of 1 share = ₹170 + ₹30 = ₹200
∴ Selling price of 50 shares = ₹(50 x 200) = ₹10000

Hence, the sale proceeds = ₹10000

(ii) Market Value of new shares = ₹125

∴ No. of new shares

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{10000}{125} \\[0.5em] = \bold{80}$

Hence, the number of ₹125 shares he buys = 80

(iii) The change in his annual income:

Annual Dividend from 10% ₹100 shares at ₹170
= No. of shares x Rate of Dividend x Nominal Value per share

$= 50 \times \dfrac{10}{100} \times 100 \\[0.5em] = \bold{₹500}$

Annual Dividend from 12% ₹100 shares at ₹125
= No. of shares x Rate of Dividend x Nominal Value per share

$= 80 \times \dfrac{12}{100} \times 100 \\[0.5em] = \bold{₹960}$

∴ Change in Annual Income = ₹960 - ₹500 = ₹460

Annual Income increased by ₹460

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

Answer

Total Investment = ₹4368

Nominal value per share = ₹100

Market value per share = ₹91

∴ Number of shares purchased

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{4368}{91} \\[0.5em] = \bold{48}$

Number of shares worth (face value) ₹2400

$= \dfrac{2400}{100} \\[0.5em] = 24$

Hence, the person sold 24 shares at ₹95.

∴ The selling value of 24 shares at ₹95 each
= ₹(24 x 95) = ₹2280

The number of remaining shares = 48 - 24 = 24

Hence, the person sold the remaining 24 shares at ₹85.

∴ The selling value of 24 shares at ₹85 each
= ₹(24 x 85) = ₹2040

∴ Total selling value = ₹2280 + ₹2040 = ₹4320

Total Gain/Loss = New Selling Value - Initial Investment
= ₹4320 - ₹4368 = -₹48

As new selling value is less than initial investment hence there is a loss of ₹48 on the total transaction.

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

Answer

Let the rate percent company is paying be x%

Dividend on 1 share of ₹50

$= x$% $\text{of ₹50}$

$= \dfrac{x}{100} \times 50 \\[0.5em] = \dfrac{x}{2}$

His profit on one share

$= 4$% $\text{of ₹80}$

$= \dfrac{4}{100} \times 80 \\[0.5em] = \dfrac{32}{10} \\[0.5em] = \dfrac{16}{5}$

As per the given,

$\dfrac{x}{2} = \dfrac{16}{5} \\[0.5em] \Rightarrow x = \dfrac{16 \times 2}{5} \\[0.5em] \Rightarrow x = 6.4$

∴ Rate percent company is paying = 6.4%

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

$= 200 \times \dfrac{6.4}{100} \times 50 \\[0.5em] = 200 \times \dfrac{64}{1000} \times 50 \\[0.5em] = 2 \times 64 \times 5 \\[0.5em] = \bold{₹640}$

∴ Dividend if he buys 200 shares = ₹640

₹100 shares of a company are sold at a discount of ₹20. If the return on the investment is 15%. Find the rate of dividend declared.

Answer

Let Rate of Dividend be x%

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

Since the shares are sold at a discount of ₹20,
Market Value of 1 share = ₹100 - ₹20 = ₹80

$$

As per the given,

$15 = \dfrac{x}{80} \times 100 \\[0.5em] x = \dfrac{15 \times 80}{100} \\[0.5em] x = 12$

∴ Rate of Dividend = 12%

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

Answer

Let the market value of 1 share be ₹x

Dividend on 1 share of ₹50 = 14% of ₹50 = ₹7

$$

As per the given,

$10 = \dfrac{7}{x} \times 100 \\[0.5em] x = \dfrac{7 \times 100}{10} \\[0.5em] x = 70$

∴ Market Value of each ₹50 share = ₹70

A company with 10000 shares of ₹100 each, declares an annual dividend of 5%.

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

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

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

Answer

(i)
Number of shares = 10000

Nominal value per share = ₹100

Rate of Dividend = 5%

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

$= 10000 \times \dfrac{5}{100} \times 100 \\[0.5em] = \bold{₹50000}$

∴ Total amount of dividend paid by the company = ₹50000

(ii)
Number of shares the man has = 72

$\text{Annual Inc.} = 72 \times \dfrac{5}{100} \times 100 \\[0.5em] = \bold{₹360}$

∴ Annual income of man with 72 shares = ₹360

(iii)
Let price paid by man for each share be ₹x

His total investment = ₹72x

$$

As per the given,

$4 = \dfrac{360}{72x} \times 100 \\[0.5em] x = \dfrac{360 \times 100}{4 \times 72} \\[0.5em] x = 125$

∴ Price paid by man for each share = ₹125

A man sold some ₹100 shares paying 10% dividend at a discount of 25% and invested the proceeds in ₹100 shares paying 16% dividend quoted at ₹80 and thus increased his income by ₹2000. Find the number of shares sold by him.

Answer

Let the number of shares sold by the man be x

The man sold the shares at a discount of 25%,
∴ Selling price of the shares = ₹100 - 25% of ₹100 = ₹100 - ₹25 = ₹75

Sales proceeds = ₹75x

Number of ₹100 16% shares purchased by the man

$= \dfrac{75x}{80} \\[0.5em] = \dfrac{15x}{16}$

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

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

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

$= \dfrac{15x}{16} \times \dfrac{16}{100} \times 100 \\[0.5em] = \bold{₹15x}$

As per the given,

$15x - 10x = 2000 \\ 5x = 2000 \\ x = 400$

∴ Number of shares sold by the man = 400

A man invests ₹6750, partly in shares of 6% at ₹140 and partly in shares of 5% at ₹125. If his total income is ₹280, how much has he invested in each ?

Answer

Let the investment of the man in shares of 6% at ₹140 be ₹x, then his investment in shares of 5% at ₹125 = ₹(6750 - x)

$\text{Income on 1 share of ₹140} = 6$% $\text{ of ₹100} = ₹6$

$\text{Income on ₹x} = ₹\dfrac{6}{140}x = ₹\dfrac{3}{70}x$

$\text{Income on 1 share of ₹125} = 5$% $\text{ of ₹100} = ₹5$

$\text{Income on ₹(6750 - x)} = ₹\dfrac{5}{125}(6750 - x) = ₹\dfrac{1}{25}(6750 - x)$

But the total income of the man is ₹280,

$\therefore \dfrac{3}{70}x + \dfrac{1}{25}(6750 - x) = 280 \\[0.5em] \Rightarrow \dfrac{3}{70}x + \dfrac{1}{25}(6750 - x) = 280 \\[0.5em] \Rightarrow \dfrac{15x + 94500 - 14x}{350} = 280 \\[0.5em] \Rightarrow x + 94500 = 280 \times 350 \\[0.5em] \Rightarrow x = 98000 - 94500 \\[0.5em] \Rightarrow x = 3500 \\[0.5em] \therefore 6750 - x = 6750 - 3500 = 3250$

∴ Investment in 6% shares at ₹140 = ₹3500
and Investment in 5% shares at ₹125 = ₹3250

Divide ₹20304 into two parts such that if one part is invested in 9% ₹50 shares at 8% premium and the other part is invested in 8% ₹25 shares at 8% discount, then the annual incomes from both the investment are equal.

Answer

Let the investment in 9% ₹50 shares be ₹x, then the investment in 8% ₹25 shares = ₹(20304 - x)

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

8% ₹25 shares are at 8% discount
∴ Market Value of one 8% ₹25 share = ₹25 - 8% of ₹25 = ₹23

$\text{Income on 1 share of ₹54} = 9$

But the annual incomes from both the investments should be equal

$\therefore \dfrac{x}{12} = \dfrac{2}{23}(20304 - x) \\[0.5em] \Rightarrow 23x = 487296 - 24x \\[0.5em] \Rightarrow 47x = 487296 \\[0.5em] \Rightarrow x = \dfrac{487296}{47} \\[0.5em] \Rightarrow x = 10368 \\[0.5em] \therefore (20304 -x) = 20304 - 10368 = 9936$

∴ Investment in 9% ₹50 shares at ₹54 = ₹10368
and Investment in 8% ₹25 shares at ₹23 = ₹9936