## Exercise 3

#### Question 1

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

**Answer**

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.

**Answer**

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.

**Answer**

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****Dividend Received = ₹160**

#### Question 4

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

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

#### 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?

**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

$= 50 \times 132 \\ = 6600$

**∴ 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

Extra shares Salman should buy

= 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?

**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

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

#### 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.

**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**

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

#### 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.

**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

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

#### 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.

**Answer**

Nominal Value per share = ₹100

Rate of Dividend = 15%

Total Investment = ₹36000

As Amit Kumar 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

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

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

#### 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.

**Answer**

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

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

Number of shares he buys

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

**∴ 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.

**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**

#### 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.

**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%**

#### 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.

**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**

#### 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.

**Answer**

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.

**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

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

**∴ 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.

**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

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

#### 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.

**Answer**

(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.

**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**

#### 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?

**Answer**

(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

(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.

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

**∴ 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?

**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**

#### 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?

**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.**

#### Question 23

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.**

#### 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.

**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**

#### 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.

**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.**

#### 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?

**Answer**

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.

**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

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

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%.

**Answer**

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%?

**Answer**

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%?

**Answer**

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.

**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

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

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.

**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**

#### 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?

**Answer**

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 ?

**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)

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

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.

**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

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

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

- 110
- 120
- 130
- 150

**Answer**

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

- 640
- 384
- 320
- 160

**Answer**

Nominal Value per share = ₹50

As Nisha buys the shares at a premium of 20%,

∴ 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

- ₹11200
- ₹14000
- ₹16800
- ₹8400

**Answer**

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

- ₹48
- ₹480
- ₹600
- ₹1200

**Answer**

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

- ₹3000
- ₹2880
- ₹1500
- ₹1440

**Answer**

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

- 80
- 400
- 600
- 800

**Answer**

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

- 10%
- 12%
- 15%
- 18%

**Answer**

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.

**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**

#### Question 2

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

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

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

#### 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.

**Answer**

(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%?

**Answer**

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.

**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

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

#### 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.

**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**

#### 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.

**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

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

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?

**Answer**

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.

**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,

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

#### 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.

**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

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

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%**