SChand CLASS 10 Chapter 3 Shares and Dividends Exercise 3B

 Exercise 3(B)

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Q1 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 1

Find the number of shares that can be bought and the income obtained by investing:

(i) Rs. 50 in (Rs. 1) shares at Rs. 1.25 paying 8%. (ii) Rs. 240 in (Rs. 5) shares at Rs. 8 paying 9%.

Sol :

(i) Cost of bought (Re. 1) shares at Rs. 1.25 = Rs 50

No of bought Shares $=\frac{50}{1.25}$ = 40 Shares.

Nominal Value of Investment = 40 Shares×Re. 1 = Rs. 40

Income obtained by Investing $= 40 \times \frac{8}{100}$ = Rs. 3.20.


(ii) Cost of bought (Rs. 5) shares at Rs. 8 = Rs 240

No of bought Shares $= \frac{240}{8}$ = 30 Shares.

Nominal Value of Investment = 30 Shares×Rs. 5 = Rs. 150

Income obtained by Investing $= 150 \times \frac{9}{100}$ = Rs. 13.50.

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Q2 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 2

A man bought 160 (Rs. 5) shares for Rs. 360. At what price did the shares stand? At what premium or discount were they quoted?

Sol :

A man bought 160 (Rs. 5) shares for Rs 360.

Price of the Shares Stand $= \frac{360}{160}$ = Rs. 2.25

Discount Rate per share = Rs. 5 – Rs. 2.25 = Rs. 2.25

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Q3 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 3

A man sold 600 (Rs. 1) shares for Rs. 750. At what price did the shares stand? At what premium or discount were they quoted?

Sol :

A man bought 600 (Rs. 1) shares for Rs 750.

Price of the Shares Stand $= \frac{750}{600}$= Rs. 1.25

Premium Rate per Share = Rs. 1.25 – Rs. 1 = Rs. 0.25 

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Q4 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 4

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

Sol :

Cost of bought 200 (₹ 10) shares at ₹ 12.50 each

Cost of bought 200 shares = 200×₹ 12.50 = ₹ 2,500.

Nominal value of investment = 200 shares×₹ 10 = ₹ 2,000.

The dividend received in cash $= ₹ 2,000 \times \frac{8}{100}$= ₹ 160.

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Q5 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 5

A man bought 500 shares, each of face value Rs. 10 of a certain business concern, and during the first year after purchase received Rs. 400 as dividend on his shares. Find the rate of dividend on his shares.

Sol :

Face value of bought 500 shares = 500×₹ 10 = ₹ 5,000

Dividend received on bought 500 shares = ₹ 400

The rate of dividend received $= ₹ 400 \times \frac{ 100 }{5000 }$= 8%.

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Q6 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 6

By purchasing Rs. 25 shares for Rs. 40 each a man gets 4 % profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares?

Sol :

Purchasing ₹ 25 shares for ₹ 40 each and gets 4% profit on his investment.

Profit (Dividend) on 1 shares $= ₹ 25 \times \frac{4}{100}$ = Rs. 1.60.

The paying rate $= ₹ 1.60\times \frac{100}{₹ 1.60}$= 6.4%.

Dividend on 60 shares = 60×₹ 1.60 = ₹ 96.

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Q7 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 7

Mukul invests Rs. 9000 in a company paying a dividend of 6% per annum when a share of face value 100 stands at Rs. 150. What is his annual income? He sells 50 % of his shares when the price rises to Rs. 200. What is his gain on this transaction?

Sol :

Cost of bought (₹ 100) shares at ₹ 150 = ₹ 9,000

No. of bought shares $=\frac{₹9,000}{₹500}$= 60 Shares

Nominal value of investment = 60 shares×₹ 100 = ₹ 6,000

The income obtained by investing $= ₹ 6,000 \times \frac{6}{100}$= ₹ 360

Cost of sale of 50% shares = 30 shares×₹ 150 = ₹ 4,500

Selling price of 50% shares = 30 shares×₹ 200 = ₹ 6,000

Gain on sale of 50% shares = S.P. – C.P. = 6,000 – 4,500 = ₹ 1,500.

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Q8 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 8

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

Sol :

Nominal value of shares $=\text{Dividend on shares} \times \frac{100}{\text{Rate of dividend}}$ $= ₹ 500 \times \frac{100}{10}$= ₹ 5,000

No. of shares purchased $= \frac{\text{Nominal value of shares}}{\text{Face Value per share}}$ $=\frac{₹ 5,000 }{100}$ = 50 Shares

Cost of 50 shares = ₹ 7,500

Price paid per share to the company $= \frac{₹ 7,500 }{50}$= ₹ 150.

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Q9 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 9

Arun owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate: (i) the dividend Arun would receive, and (ii) the rate of interest, on his investment. Considering that Arun bought these shares @Rs. 30 per share in the market.

Sol :

(i) Nominal value of shares = No. of shares X Nominal value per share = 560×₹ 25 = ₹ 14,000

Dividend on shares $= \text{Nominal value of shares} \times \frac{\text{Rate of dividend}}{100}$ $= 14,000 \times \frac{ 9}{ 100}$ = ₹ 1,260


(ii) If Arun bought these 560 shares @ ₹ 30 per share in the market.

Cost of investment = 560 shares×₹ 30 = ₹ 16,800

Income on investment = ₹ 1,260

Interest on investment $= 1,260 \times \frac{100}{16,800} =7\frac{1}{2}$%.

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Q10 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 10

What sum should Ashok invest in Rs 25 shares selling at Rs 36 to obtain an income of Rs. 720, if the dividend declared is 12%. Also find (i) the number of shares bought by Ashok (ii) the percentage return on his investment.

Sol :

Nominal value of shares $= Dividend on shares \times \frac{100}{ Rate of dividend}$

$= 720 \times \frac{100}{ 12 }$ = ₹ 6,000

No. of shares purchased $= \frac{\text{Nominal value of shares}}{\text{ Face value per share}$ $=\frac{6,000}{ 25}$ = 240 shares

Sum paid for investment = 240 shares×₹ 36 = ₹ 8,640

Return on investment $= \text{Annual income from shares } \times \frac{100}{\text{Cost of Investment}$ $= 720\times \frac{100}{8,640}$= 8.33%

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Q11 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 11

Mr. Sharma has 60 shares of nominal value of Rs. 100 and he decides to sell them when they are at a premium of 60%. He invests the proceeds in shares of nominal value Rs. 50 quoted at 4% discount, paying 18% dividend annually. Calculate: (i) the sale proceeds (ii) the number of shares he buys (iii) the annual dividend from these shares

Sol :

(i) Sales proceeds of 60 shares = Nominal value of 60 shares + 60% Premium = ( 60 x 100 ) + 60% of ₹ 6,000 = 6,000 + 3,600 = ₹ 9,600.

(ii) Rate per new share = ₹ 50 – 4% Discount 0f ₹ 50 = 50 – 2 = ₹ 48

No. of purchased new shares $= \frac{₹ 9,600 }{ 48}$= 200 shares

(iii) Nominal value of shares = No. of shares×Nominal value per share = 200×₹ 50 = ₹ 10,000

Annual dividend on shares $=\text{ Nominal value of shares }\times \frac{\text{Rate of dividend} }{ 100 }$ $= 10,000 \times \frac{18 }{100}$ = ₹ 1,800.

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Q12 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 12

A man invests a sum of money in Rs. 100 shares, paying 15% dividend, quoted at 20% premium. If his annual dividend is Rs. 540, calculate (i) his total investment, (ii) the rate of return of his investment.

Sol :

Nominal value of shares $= Dividend on shares \times \frac{100}{ Rate of dividend}$

$= ₹ 540 \times \frac{100}{ 15}$ = ₹ 3,600

(i) Cost of total investment = Nominal value of shares + 20% Premium = ₹ 3,600 + 20% of ₹ 3,600 = 3,600 + 720 = ₹ 4,320.

(ii) Rate of return on investment $= \text{Annual dividend on shares } \time \frac{100}{ \text{Cost of Investment }}$ $= 540 \times \frac{ 100 }{4,320}$= 12.5%

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Q13 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 13

A lady holds 1800 hundred rupee 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 would she have got on her investment? Give your answer to the nearest integer.

Sol :

Nominal value of shares = No. of shares×Nominal value per share = 1,800×₹ 100 = ₹ 1,80,000

Annual dividend on shares $= \text{Nominal value of shares} \times \frac{\text{Rate of dividend}}{ 100}$ $= 1,80,000 \times \frac{15}{100}$= ₹ 27,000.

Cost of total investment = Nominal value of shares + 40% Premium = ₹ 1,80,000 + 40% of ₹ 1,80,000 = 1,80,000 + 72,000 = ₹ 2,52,000

Rate of return on investment $= \text{Annual dividend on shares}\times \frac{100 }{Cost of Investment}$ $= 27,000\times \frac{100}{ 2,52,000}$ = 10.71% = 11% ( to the nearest integer ).

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Q14 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 14

A man invests Rs. 11200 in a company paying 6% dividend when its Rs. 100 share can be bought for Rs. 140. Find (i) his annual income. (ii) the percentage income on his investment.

Sol :

(i) Cost of bought (₹ 100) shares at ₹ 140 = ₹ 11,200

No. of bought shares $= \frac{₹ 11,200 }{₹ 140 }$= 80 Shares

Nominal value of investment = 80 shares×₹ 100 = ₹ 8,000

∴ The income obtained by investing $= ₹ 8,000 \times \frac{6}{100}$ = ₹ 480

(ii) Rate of return on investment $= \text{Annual dividend on shares} \times \frac{100}{\text{Cost of Investment}}$ $= 480\times \frac{100}{11,200}$= 4 2/7%.

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Q15 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 15

A company with 10000 shares of Rs. 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% of his investment, find the price he had paid for each share.

Sol :

(i) Nominal value of shares in the company = No. of shares×Nominal value per share = 10,000×₹ 100 = ₹ 10,00,000

∴ Annual dividend paid by the company $=\text{Nominal value of shares}\times \frac{\text{Rate of dividend}}{100}$ $= 10,00,000 \times \frac{5}{100}$ = ₹ 50,000

(ii) Nominal value of 72 shares = No. of shares×Nominal value per share = 72×₹ 100 = ₹ 7,200

∴ Annual income of a man on 72 shares $= \text{Nominal value of shares} \times \frac{\text{Rate of dividend}}{100 }$= 7,200×5100 = ₹ 360

(iii) Income on investment at 4% $= 7,200 \times \frac{4}{100}$= 288

Price paid for each share $= Annual dividend on shares \times \frac{100}{\text{Income of Investment}}$ $= 360 \times \frac{100}{288}$= ₹ 125.

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Q16 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 16

A man invests Rs. 1680 in buying shares of nominal value of Rs. 24 and selling at 12% premium. The dividend on the shares is 15% per annum. (i) Calculate the number of shares he buys. (ii) Calculate the dividend he receives annually.

Sol :

(i) Cost of investment per share = Nominal value of shares + 12% Premium = ₹ 24 + 12% of ₹ 24 = 24 + 2.88 = ₹ 26.88

Cost of total investment = ₹ 1,680

No. of purchased shares $=\frac{ ₹ 1,680 }{26.88}$ = 62.5 Shares

(ii) Nominal value of 62.5 shares = No. of shares×Nominal value per share = 62.5×₹ 24 = ₹ 1,500

∴ Annual dividend received on shares $= \text{Nominal value of shares} \times \frac{\text{Rate of dividend }}{100}$ $=\frac{ 1,500 \times 15 }{100}$ = ₹ 225.

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Q17 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 17

A man invests Rs. 7425 on buying shares of face value of Rs. 90 each at a premium of 10% in a company. If he earns Rs. 1350 as dividend at the end of the year, find (i) the number of shares he has in the company. (ii) the dividend percentage per share that he received.

Sol :

(i) Cost of investment per share = Face value per shares + 10% Premium = ₹ 90 + 10% of ₹ 90 = 90 + 9 = ₹ 99

Cost of total investment = ₹ 7,425

No. of purchased shares $= \frac{₹ 7,425}{99}$= 75 shares

(ii) Nominal value of 75 shares = No. of shares×Nominal value per share = 75×₹ 90 = ₹ 6,750

Dividend percentage per share $= \text{Annual dividend on shares }\times \frac{ 100}{\text{Nominal Value}}$= 1,350 X 100 / 6,750 = 20%.

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Q18 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 18

Abhishek sold a certain number of shares of Rs. 20 paying 8% dividend at Rs. 18 and invested the proceeds in Rs. 10 shares, paying 12% dividend at 50 % premium. If the change in his annual income is Rs. 120, find the number of shares sold by him?

Sol :

Let, Abhishek sell X shares.

Selling price of X shares = X×₹ 18 = 18X

Face value of X shares = X×₹ 20 = 20X

Dividend on X shares = 8% of 20X $= 20X \times \frac{8}{100} =\frac{ 8X}{5}$

Now, Rate per new share = ₹ 10 + 50% Premium = 10 + 5 = 15

No. of purchased new shares = Sale Proceeds / Rate per new share $= \fac{18X}{15}= \frac{6X}{5}$

Nominal value of purchased new shares $= \frac{6X}{5} \times 10$ = 12X

Dividend on purchased new shares = 12% of 12X $= 12X \times \frac{12}{100} =\frac{ 36X}{25}$

Change in annual income = ₹ 120

$\frac{8X}{5}− \frac{36X}{25} = 120$

⇒ X = 750

No. of shares sold by Abhishek = X = 750 shares

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Q19 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 19

A person invested Rs. 8000 and Rs. 10000 in buying shares of two companies which later on declared dividends of 12% and 8% respectively. He collects the dividends and sells out his shares at a loss of 2% and 3% respectively. Find his total earning from the above transaction.

Sol :

Dividend received = 12% of ₹ 8,000 + 8% of ₹ 10,000 = 960 + 800 = ₹ 1,760

Loss on sale of shares=2% of ₹8,000 + 3% of ₹ 10,000 = 160 + 300 = ₹ 460

∴Total earning = Dividend received – Loss on sale of shares = 1,760 – 460 = ₹ 1,300

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Q20 | Ex-3B | Class 8 | S.Chand | Mathematics | Chapter 3 | Shares and Dividends | myhelper

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Question 20

A person invested 20%, 30% and 25% of his saving in buying shares of three different companies A, B and C, which declared dividends of 10%, 12% and 15% respectively. If his total income on account of dividends be Rs. 2337.50, find his saving and the amount which he invested in buying shares of each company.

Sol :

Let, Total saving be X.

Dividend received = 10% of (20% of X) + 12% of (30% of X) + 15% of (25% of X)

⇒$2,337.50 = \frac{X}{50} +\frac{ 9X}{250} + \frac{3X}{80}$

⇒ X = 25000

Total saving = X = ₹ 25,000

Investment in company ‘A’ = 20% of ₹ 25,000 = ₹ 5,000

Investment in company ‘B’ = 30% of ₹ 25,000 = ₹ 7,500

Investment in company ‘C’ = 25% of ₹ 25,000 = ₹ 6,250