# Shares and Dividends

## Exercise 3

#### Question 1

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

Dividend on 1 share

$= 9\% \text{ of ₹20} \\[0.5em] = \dfrac{9}{100} \times 20 \\[0.5em] = ₹1.8$

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

#### Question 2

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.

Let nominal value of shares be ₹x

According to the given,

$8\% \text{ of } x = 2840 \\[0.5em] \Rightarrow \dfrac{8}{100} \times x = 2840 \\[0.5em] \Rightarrow x = \dfrac{2840 \times 100}{8} \\[0.5em] \Rightarrow x = 35500$

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

#### Question 3

A man buys 200 ten-rupee shares at ₹12.50 each and receives a dividend of 8%. Find the amount invested by him and the dividend received by him in cash.

Nominal Value of 1 share = ₹10

Market Value of 1 share = ₹12.50

Number of shares purchased = 200

Amount Invested = No. of shares x Market Value
= 200 x 12.50
= ₹2500

Nominal Value of 200 shares = 200 x 10
= 2000

Rate of dividend = 8%

∴ Dividend received = 8% of 2000

$= \dfrac{8}{100} \times 2000 \\[0.5em] = 160$

Hence,
Amount invested = ₹2500

#### Question 4

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

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

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

#### Question 5

Salman 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?

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

$= 50 \times 132 \\ = 6600$

∴ Salman's investment = ₹6600

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

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

∴ Salman's 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

= 70 - 50
= 20

#### Question 6

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?

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{27000}{252000} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{2700}{252} \Big) \% \\[0.5em] = \Big(\dfrac{75}{7} \Big) \% \\[0.5em] = \bold{10\frac{5}{7}\%}$

#### Question 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.

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{720}{8640} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{72000}{8640} \Big) \% \\[0.5em] = \Big(\dfrac{25}{3} \Big) \% \\[0.5em] = \bold{8\frac{1}{3}\%}$

#### Question 8

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.

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

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

#### Question 9

Amit Kumar 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.

Nominal Value per share = ₹100

Rate of Dividend = 15%

Total Investment = ₹36000

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

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{4500}{36000} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{450000}{36000} \Big) \% \\[0.5em] = \Big(\dfrac{25}{2} \Big) \% \\[0.5em] = \bold{12.5\%}$

#### Question 10

Mr. Tiwari invested ₹29040 in 15% ₹100 shares at a premium of 20%. Calculate:

(i) the number of shares bought by Mr. Tiwari

(ii) Mr. Tiwari's income from the investment

(iii) the percentage return on his investment.

Nominal Value per share = ₹100

Rate of Dividend = 15%

Total Investment = ₹29040

(i)
As Mr. Tiwari bought the shares at 20% premium,

Market Value of one share

$= 100 + \Big(\dfrac{20}{100} \times 100\Big) \\[0.5em] = 100 + 20 \\[0.5em] = ₹120$

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{29040}{120} \\[0.5em] = \bold{242}$

∴ Number of shares bought by Mr. Tiwari = 242

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

$= 242 \times \dfrac{15}{100} \times 100 \\[0.5em] = \bold{₹3630}$

∴ Mr. Tiwari's income from the investment = ₹3630

(iii)
$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{3630}{29040} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{363000}{29040} \Big) \% \\[0.5em] = \Big(\dfrac{25}{2} \Big) \% \\[0.5em] = \bold{12.5\%}$

∴ Percentage return on his investment = 12.5%

#### Question 11

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.

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

#### Question 12

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.

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%

#### Question 13

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.

(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

#### Question 14

A company pays a dividend of 15% on its ten-rupee shares from which it deducts tax at the rate of 22%. Find the annual income of a man who owns one thousand shares of this company.

Nominal Value per share = ₹10

Rate of Dividend = 15%

No. of shares owned = 1000

Tax Rate = 22%

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

$= 1000 \times \dfrac{15}{100} \times 10 \\[0.5em] = ₹1500$

Tax = 22% of ₹1500

$= \dfrac{22}{100} \times 1500 \\[0.5em] = ₹330$

Annual Income = Annual Dividend - Tax
= 1500 - 330
= ₹1170

∴ Annual Income of man after the deduction = ₹1170

#### Question 15

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.

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{1260}{16800} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{1260}{168} \Big) \% \\[0.5em] = \Big(\dfrac{15}{2} \Big) \% \\[0.5em] = \bold{7\frac{1}{2}\%}$

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

#### Question 16

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.

(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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{720}{13500} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{720}{135} \Big) \% \\[0.5em] = \Big(\dfrac{16}{3} \Big) \% \\[0.5em] = \bold{5\frac{1}{3}\%}$

#### Question 17

A company with 4000 shares of nominal value of ₹110 declares annual dividend of 15%. Calculate :

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

(ii) the annual income of Shah Rukh who holds 88 shares in the company.

(iii) if he received only 10% on his investment, find the price Shah Rukh paid for each share.

(i)
No. of shares = 4000

Nominal Value per share = ₹110

Rate of Dividend = 15%

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

$= 4000 \times \dfrac{15}{100} \times 110 \\[0.5em] = ₹66000$

∴ Total amount of dividend paid by the company = ₹66000

(ii)
No. of shares held by Shahrukh = 88

Nominal Value per share = ₹110

Rate of Dividend = 15%

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

$= 88 \times \dfrac{15}{100} \times 110 \\[0.5em] = ₹1452$

∴ Annual income of Shahrukh = ₹1452

(iii)
Let the price Shahrukh paid for each share be x

Total investment of Shahrukh = ₹88x

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] 10 = \Big(\dfrac{1452}{88x} \times 100\Big) \% \\[0.5em] x = \dfrac{14520}{88} \\[0.5em] x = \bold{165}$

∴ Price Shahrukh paid for each share = ₹165

#### Question 18

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

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

#### Question 19

A man invests ₹8000 in a company paying 8% dividend, when a share of face value of ₹100 is selling at ₹60 premium.

(i) What is his annual income?

(ii) What percent does he get on his money?

(i)
Nominal Value per share = ₹100

Rate of Dividend = 8%

Total Investment = ₹8000

As the shares are selling at ₹60 premium,

Market Value per share = ₹100 + ₹60 = ₹160

∴ Number of shares he buys

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{8000}{160} \\[0.5em] = \bold{50}$

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

$= 50 \times \dfrac{8}{100} \times 100 \\[0.5em] = \bold{₹400}$

∴ Annual income = ₹400

(ii)
$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{400}{8000} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{40}{8} \Big) \% \\[0.5em] = \bold{5\%}$

∴ Percent he gets on his money = 5%

#### Question 20

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

(iii) yield.

(i)
Number of shares = 400

Nominal Value per share = ₹10

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

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

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{320}{5000} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{32}{5} \Big) \% \\[0.5em] = \bold{6.4\%}$

∴ Yield = 6.4%

#### Question 21

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?

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

#### Question 22

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

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.

#### Question 23

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

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.

#### Question 24

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.

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

#### Question 25

A man bought 360 ten-rupee shares paying 12% per annum. He sold them when the price rose to ₹21 and invested the proceeds in five-rupee shares paying 4½% per annum at ₹3.5 per share. Find the annual change in his income.

Answer Number of shares = 360

Nominal value per share = ₹10

Rate of Dividend = 12%

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

$= 360 \times \dfrac{12}{100} \times 10 \\[0.5em] = \bold{₹432}$

∴ Annual Income from previous shares = ₹432

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

Selling price of 1 share = ₹21
∴ Selling price of 360 shares = ₹(360 x 21) = ₹7560

Hence, sale proceeds = ₹7560

Total Investment in new shares = Sale Proceeds = ₹7560

Market Value per share of new shares = ₹3.5

∴ No. of new shares

$= \dfrac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \dfrac{7560}{3.5} \\[0.5em] = \bold{2160}$

Nominal value per share of new shares = ₹5

Rate of Dividend of new shares = 4½%

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

$= 2160 \times \dfrac{4\frac{1}{2}}{100} \times 5 \\[0.5em] = 2160 \times \dfrac{9}{200} \times 5 \\[0.5em] = \bold{₹486}$

∴ Change in Annual Income = ₹486 - ₹432 = ₹54

Annual Income increased by ₹54

#### Question 26

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.

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.

#### Question 27

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?

Let the rate percent company is paying be x%

Dividend on 1 share of ₹50

$= \text{x\% of ₹50} \\[0.5em] = \dfrac{x}{100} \times 50 \\[0.5em] = \dfrac{x}{2}$

His profit on one share

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

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

#### Question 28

₹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.

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em]$

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%

#### Question 29

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

Let the market value of 1 share be ₹x

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em]$

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

#### Question 30

At what price should a 6.25% ₹100 share be quoted when the money is worth 5%?

Let the market value of 1 share be ₹x

Dividend on 1 share of ₹100 = 6.25% of ₹100 = ₹6.25

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em]$

As per the given,

$5 = \dfrac{6.25}{x} \times 100 \\[0.5em] x = \dfrac{6.25 \times 100}{5} \\[0.5em] x = 125$

∴ ₹100 share should be quoted at ₹125

#### Question 31

At what price should a 6.25% ₹50 share be quoted when the money is worth 10%?

Let the market value of 1 share be ₹x

Dividend on 1 share of ₹50 = 6.25% of ₹50 = ₹3.125

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em]$

As per the given,

$10 = \dfrac{3.125}{x} \times 100 \\[0.5em] x = \dfrac{3.125 \times 100}{10} \\[0.5em] x = 31.25$

∴ ₹50 share should be quoted at ₹31.25

#### Question 32

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.

(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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em]$

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

#### Question 33

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.

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

#### Question 34

By selling at ₹77, some 2¼% shares of face value ₹100, and investing the proceeds in 6% shares of face value ₹100, selling at ₹110, a person increased his income by ₹117 per annum. How many shares did he sell?

Let the number of shares sold by the man be x

Selling price of one share = ₹77
∴ Sales proceeds = ₹77x

Number of ₹100 6% shares purchased by the man

$= \dfrac{77x}{110} \\[0.5em] = \dfrac{7x}{10}$

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

$= x \times \dfrac{2\frac{1}{4}}{100} \times 100 \\[0.5em] = \bold{₹\dfrac{9x}{4}}$

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

$= \dfrac{7x}{10} \times \dfrac{6}{100} \times 100 \\[0.5em] = \bold{₹\dfrac{21x}{5}}$

As per the given,

$\dfrac{21x}{5} - \dfrac{9x}{4} = 117 \\[0.5em] \Rightarrow \dfrac{84x - 45x}{20} = 117 \\[0.5em] \Rightarrow \dfrac{39x}{20} = 117 \\[0.5em] \Rightarrow x = \dfrac{117 \times 20}{39} \\[0.5em] \Rightarrow x = 60 \\[0.5em]$

∴ Number of shares sold by the man = 60

#### Question 35

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 ?

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)

$\text{Income on 1 share of ₹140} = 6\% \text{ of ₹100} = ₹6 \\[0.5em] \text{Income on ₹x} = ₹\dfrac{6}{140}x = ₹\dfrac{3}{70}x \\[0.5em] \text{Income on 1 share of ₹125} = 5\% \text{ of ₹100} = ₹5 \\[0.5em] \text{Income on ₹(6750 - x)} = ₹\dfrac{5}{125}(6750 - x) = ₹\dfrac{1}{25}(6750 - x) \\[0.5em]$

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

#### Question 36

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.

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

$\text{Income on 1 share of ₹54} = 9\% \text{ of ₹50} = ₹4.50 \\[0.5em] \text{Income on ₹x} = ₹\dfrac{4.5}{54}x = ₹\dfrac{x}{12} \\[0.5em] \text{Income on 1 share of ₹23} = 8\% \text{ of ₹25} = ₹2 \\[0.5em] \text{Income on ₹(20304 -x)} = ₹\dfrac{2}{23}(20304 - x) \\[0.5em]$

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

## Multiple Choice Questions

#### Question 1

If Jagbeer invest ₹10320 on ₹100 shares at a discount of ₹14, then the number of shares he buys is

1. 110
2. 120
3. 130
4. 150

Nominal Value per share = ₹100

As Jagbeer buys the shares at a discount of ₹14,
∴ Market Value per share = ₹100 - ₹14 = ₹86

Jagbeer's Total Investment = ₹10320

$\therefore \text{No. of shares} = \dfrac{\text{Investment}}{\text{M.V.}} \\[0.5em] = \dfrac{10320}{86} = 120$

∴ Option 2 is the correct option.

#### Question 2

If Nisha invests ₹19200 on ₹50 shares at a premium of 20%, then the number of shares she buys is

1. 640
2. 384
3. 320
4. 160

Nominal Value per share = ₹50

∴ Market Value per share = ₹50 + 20% of ₹50 = ₹50 + ₹10 = ₹60

Nisha's Total Investment = ₹19200

$\therefore \text{No. of shares} = \dfrac{\text{Investment}}{\text{M.V.}} \\[0.5em] = \dfrac{19200}{60} = 320$

∴ Option 3 is the correct option.

#### Question 3

₹40 shares of a company are selling at 25% premium. If Mr. Jacob wants to buy 280 shares of the company, then the investment required by him is

1. ₹11200
2. ₹14000
3. ₹16800
4. ₹8400

Nominal Value per share = ₹40

As the shares are selling at 25% premium,
∴ Market Value per share = ₹40 + 25% of ₹40 = ₹40 + ₹10 = ₹50

No of shares Mr. Jacob wants to buy = 280

∴ Total Investment of Mr. Jacob = 280 x 50 = ₹14000

∴ Option 2 is the correct option.

#### Question 4

Arun possesses 600 shares of ₹25 of a company. If the company announces a dividend of 8%, then Arun's annual income is

1. ₹48
2. ₹480
3. ₹600
4. ₹1200

No. of shares = 600

Nominal Value per share = ₹25

Rate of Dividend = 8%

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

$= 600 \times \dfrac{8}{100} \times 25 \\[0.5em] = ₹1200$

∴ Option 4 is the correct option.

#### Question 5

A man invests ₹24000 on ₹60 shares at a discount of 20%. If the dividend declared by the company is 10%, then his annual income is

1. ₹3000
2. ₹2880
3. ₹1500
4. ₹1440

Nominal Value per share = ₹60

As the shares are bought at a discount of 20%,
∴ Market Value per share = ₹60 - 20% of ₹60 = ₹60 - ₹12 = ₹48

Total Investment = ₹24000

$\therefore \text{No. of shares} = \dfrac{\text{Investment}}{\text{M.V.}} \\[0.5em] = \dfrac{24000}{48} = 500$

Rate of Dividend = 10%

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

$= 500 \times \dfrac{10}{100} \times 60 \\[0.5em] = ₹3000$

∴ Option 1 is the correct option.

#### Question 6

Salman has some shares of ₹50 of a company paying 15% dividend. If his annual income is ₹3000, then the number of shares he possesses is

1. 80
2. 400
3. 600
4. 800

Let the number of shares Salman owns be x

Nominal Value per share = ₹50

Rate of Dividend = 15%

Annual Dividend = ₹3000

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

According to the given,

$3000 = x \times \dfrac{15}{100} \times 50 \\[0.5em] 3000 = \dfrac{15x}{2} \\[0.5em] x = \dfrac{3000 \times 2}{15} \\[0.5em] x = 400$

∴ Option 2 is the correct option.

#### Question 7

₹25 shares of a company are selling at ₹20. If the company is paying a dividend of 12%, then the rate of return is

1. 10%
2. 12%
3. 15%
4. 18%

Nominal Value per share = ₹25

Market Value per share = ₹20

Rate of Dividend = 12%

Income on 1 share

$= 1 \times \dfrac{12}{100} \times 25 \\[0.5em] = 3$

$\% \text{Return} = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{3}{20} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{300}{20} \Big) \% \\[0.5em] = \bold{15\%}$

∴ Option 3 is the correct option.

## Chapter Test

#### Question 1

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

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

#### Question 2

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

Nominal Value per share = ₹10

Market Value per share = ₹12

Rate of Dividend = 18%

Dividend on 1 share

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

$\% \text{Return} = \Big(\dfrac{\text{Inc. per share}}{\text{M.V. per share}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{\frac{9}{5}}{12} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{9}{5} \times \dfrac{1}{12} \times 100 \Big) \% \\[0.5em] = \bold{15\%}$

#### Question 3

Rohit Kulkani 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.

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

Total Investment of Rohit Kulkani = ₹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)
$\% \text{Return} = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{800}{10000} \times 100\Big) \% \\[0.5em] = \bold{8\%}$

∴ Rate percent Rohit Kulkani earns on his investment = 8%

#### Question 4

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

Let the market value of 1 share be ₹x

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em]$

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

#### Question 5

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.

(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

$\% \text{Return} = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em] = \Big(\dfrac{240}{5520} \times 100\Big) \% \\[0.5em] = \Big(\dfrac{2400}{552} \Big) \% \\[0.5em] = \Big(\dfrac{100}{23} \Big) \% \\[0.5em] = \bold{4\dfrac{8}{23}\%}$

#### Question 6

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.

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

#### Question 7

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.

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

$\text{Income on 1 share of ₹92} = 8\% \text{ of ₹100} = ₹8 \\[0.5em] \text{Income on ₹x} = ₹\dfrac{8}{92}x == ₹\dfrac{2}{23}x \\[0.5em] \text{Income on 1 share of ₹54} = 9\% \text{ of ₹50} = ₹4.50 \\[0.5em] \text{Income on ₹(101520 - x)} = ₹\dfrac{4.5}{54}(101520 - x) = ₹\dfrac{101520 - x}{12} \\[0.5em]$

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

#### Question 8

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?

Let the market value of 1 share be ₹x

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

$\% Return = \Big(\dfrac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)\% \\[0.5em]$

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

#### Question 9

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.

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,

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

#### Question 10

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.

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

$= ₹40 - 20\% \text{ of } ₹40 \\[0.5em] = ₹40 - ₹\Big(\dfrac{20}{100} \times 40 \Big) \\[0.5em] = ₹40 - ₹8 \\[0.5em] = ₹32$

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

$= ₹75 + 20\% \text{ of } ₹75 \\[0.5em] = ₹75 + ₹\Big(\dfrac{20}{100} \times 75 \Big) \\[0.5em] = ₹75 + ₹15 \\[0.5em] = ₹90$

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%