SChand CLASS 10 Chapter 3 Shares and Dividends Exercise 3A

 Exercise 3(A)

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

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Question 1

(i) 200 shares of Rs. 10 each available at Rs. 2.50 premium.

(ii) 220 shares of Rs. 15 each available at Rs. 1.50 discount.

(iii) Purchasing Rs. 200 stock yielding 9% at 105.

(iv) 1000 shares of Rs 25 each at a premium of Rs. 60.

(v) 450 shares of Rs. 100 each at the market price of Rs. 30.80

Sol :

(i) Nominal Value of Shares = No of Shares×Nominal Value per share = 200×10 = Rs. 2000

Premium = No of Shares×Premium per share = 200×2.50 = Rs. 500

Cost of Share = Nominal Value of Shares + Premium = 2000 + 500 = Rs. 2500.

(ii) Nominal Value of Shares = No of Shares×Nominal Value per share =220×15 = Rs. 3300

Discount = No of Shares×Discount per share = 220×1.50 = Rs. 330

Cost of Share = Nominal Value of Shares – Discount = 3300 – 330 = Rs. 2970.

(iii) Cost of Stock = No of Stock×Rate per Stock = 200×105 = Rs. 21000.

(iv) Nominal Value of Shares = No of Shares×Nominal Value per share = 1000×25 = Rs. 25000

Premium = No of Shares×Premium per share = 1000×60 = Rs. 60000

Cost of Share = Nominal Value of Shares + Premium = 25000 + 60000 = Rs. 85000.

(v) Cost of Share = No of Shares×Market Value per Share = 450×30.80 = Rs. 13860.

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

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Question 2

(i) 450 shares with par value of Rs. 10 if the annual dividend is 7.5%.

(ii) 50 Tata Mills 4% (Rs. 6) shares at Rs. 6.25.

(iii) 180 Shri Ram Fibres 7 ½% (Rs. 10) shares at 14.50.

(iv) 100 Hindustan Motors (Rs. 10) shares at Rs. 8 dividends 4% p.a.

Sol :

(i) Nominal Value of Shares = No of Shares×Nominal Value per share = 450×10 = Rs. 4500.

Annual Dividends on Shares $=\frac{\text{ (Nominal Value of Shares×Rate of Dividend) }}{100} $

$=\frac{4500 \times 7.5}{100}$= Rs. 337.50.

(ii) Nominal Value of Shares = No of Shares×Nominal Value per share = 50×6 = Rs. 300.

Annual Dividends on Shares$ =\text{ (Nominal Value of Shares×Rate of Dividend)}{100} $

$= \frac{300 \times 4}{100}$ = Rs. 12.

(iii) Nominal Value of Shares = No of Shares×Nominal Value per share = 180×10 = Rs. 1800.

Annual Dividends on Shares $=\frac{\text{ (Nominal Value of Shares×Rate of Dividend) }}{100} $

$= 1800 \times \frac{7.5 }{100}$ = Rs. 135

(iv) Nominal Value of Shares = No of Shares × Nominal Value per share = 100×10 = Rs. 1000.

Annual Dividends on Shares $=\frac{\text{ (Nominal Value of Shares×Rate of Dividend) }}{100} $

$= 1000 \times \frac{4}{100}$ = Rs. 40.

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

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Question 3

Write down the sum of money obtained by selling 60 (Rs. 100) shares at 112.

Sol :

The sum of money obtained by selling 60 shares = No of Shares × Selling Rate per Share = 60×112 = Rs. 6720.

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

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Question 4

Ravi invested Rs. 6250 in shares of a company paying 6% per annum. If he bought Rs. 25 shares for Rs. 31.25 each, find his annual income from this investment.

Sol :

No of Share bought $=\frac{ \text{Investment} }{\text{Market Value per Share} }= \frac{6250 }{31.25 }$= 200 Shares

Nominal Value of Shares = No of Shares×Nominal Value per share = 200×25 = Rs. 5000.

Annual Dividends on Shares $=\frac{\text{ (Nominal Value of Shares×Rate of Dividend) }}{100} $

$= 5000 \times \frac{6}{100}$ = Rs. 300.

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

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Question 5

Write down the price of 100 (Rs. 10) shares costing Rs. 2000.

Sol :

Market Value per Share $= \frac{\text{Cost of Shares}}{\text{No of Shares} }= \frac{2000}{100}$ = Rs. 20.

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

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Question 6

A company declares semi-annual dividend of 5%. Krishan Lal owns 25 shares (of par value Rs. 12.50 each). How much annual dividend must be receive?

Sol :

Nominal Value of Shares = No of Shares×Nominal Value per share = 25×12.50 = Rs. 312.50.

Rate of semi-annual dividend = 5%, Rate of annual dividends = 10%

Annual Dividend $= \frac{\text{Nominal Value of Shares×Rate of Annual Dividend} }{100}$

$= 312.50 \times \frac{10}{100 }$= Rs. 31.25.

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

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Question 7

A man bought 250 (Rs. 1) shares and receive from them a dividend of Rs. 20. What is the rate % of the dividend?

Sol :

Nominal Value of Shares = No of Shares×Nominal Value per share = 250×1 = Rs. 250.

Annual of Dividend Received = Rs. 20

Rate of Dividend $= \frac{\text{Amount of Dividend Received}} \times 100}{Nominal Value of Shares }$ $= \frac{(20 \times 100)}{ 250 }= 8%.

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

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Question 8

A man invests Rs. 4800 in shares of a company which was paying 8% dividend at the time when a Rs. 100 share cost Rs. 160. Find (i) his annual income from the shares, (ii) the rate of interest he gets on his investment.

Sol :

No of Share bought $=\frac{\text{ Investment} }{ \text{Market Value per Share}} $ $=\frac{ 4800}{160}$ = 30 Shares

Nominal Value of Shares = No of Shares×Nominal Value per share = 30×100 = Rs. 3000.

Annual Dividends on Shares $=\frac{\text{ (Nominal Value of Shares×Rate of Dividend) }}{100} $

$= 3000 \times \frac{8 }{100}$ = Rs. 240.

(ii) Rate of interest he gets on his investment $= \frac{\text{Annual income from shares }\times 100 }{ Cost of investment$ $= 240\times \frac{100}{4800}$= 5%.

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

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Question 9

A company pays a dividend of 15% on its ten-rupee shares from which is deducted income tax at the rate of 22%. Find the annual income of a man who owns 100 shares of this company.

Sol :

Nominal Value of Shares = No of Shares×Nominal Value per share = 100×10 = Rs. 1000

Annual Dividend $= \frac{\text{Nominal Value of Shares×Rate of Annual Dividend} }{100}$

$= 1000 \times \frac{15}{100}$ = Rs. 150.

TDS (Tax Deducted at Sources) $= \frac{\text{Annual Dividend×Rate of Income Tax} }{100}$ $= 150\times \frac{22}{100}$= Rs. 33

Annual income of 100 shares = Annual Dividend – TDS = 150 – 33 = Rs. 117.

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

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Question 10

A man bought 1000 shares each of face value Rs 5 at Rs. 7 per value. At the end of the year, the company from which he bought the shares declares a dividend of 8%. Calculate: (i) the amount of money invested by the man. (ii) the percentage return on his outlay correct to one decimal place.

Sol :

(i) Amount of Money Invested = No of Shares×Market value per Share = 1000×7 = Rs. 7000.

(ii) Nominal Value of Shares = No of Shares×Nominal Value per share = 1000×5 = Rs. 5000

Annual Dividend $= \frac{\text{Nominal Value of Shares×Rate of Annual Dividend} }{100}$

$= 5000 \times \frac{8}{100}$ = Rs. 400.

Percentage Return on Investment $= \frac{\text{Annual Dividend} \times  100 }{ \text{Cost of Investment}} = 400 \times \frac{100}{7000}$ = 5.7%.

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

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Question 11

A company with 10000 shares of nominal value Rs. 100 declares an annual of dividends of 8% to the share-holders. (i) Calculate the total amount of dividend paid by the company (ii) Ramesh had bought 90 shares of the company at Rs. 150 per share. Calculate the dividend he receive and the percentage return on his investment.

Sol :

(i) Nominal Value of Shares = No of Shares×Nominal Value per share = 10000×100 = Rs. 1000000

Annual Dividend $= \frac{\text{Nominal Value of Shares×Rate of Annual Dividend} }{100}$

$= \frac{1000000 \times 8}{ 100 }$= Rs. 80000.

(ii) Nominal Value of Shares = No of Shares×Nominal Value per share = 90×100 = Rs. 9000.

Annual Dividend $= \frac{\text{Nominal Value of Shares×Rate of Annual Dividend} }{100}$

$= 9000 \times \frac{8}{100}$ = Rs. 720.

Percentage Return on Investment $= \frac{\text{Annual Dividend} \times  100 }{ \text{Cost of Investment}} = 720\times \frac{100}{13500}$ = 5.33%.

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

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Question 12

Aditi has 40 shares of nominal value Rs 100 and she decides to sell them when they are at a premium of 50%. She invests the proceeds in shares of nominal value of Rs. 75 quoted at 20% discount paying 25% dividend annually. Calculate (i) the sale proceeds (ii) the number of shares she buys (iii) the annual dividend from these shares.

Sol :

(i) Nominal Value of Shares = No of Shares×Nominal Value per share = 40×100 = Rs. 4000.

Sale proceeds of 40 Shares = Nominal value of Shares + 50% Premium = 4000 + (50% of 4000) = 4000 + 2000 = Rs. 6000.

(ii) No of Shares $= \frac{\text{Amount Invested in New Shares }}{ \text{(Rate of New Share – Discount) }}$ $= \frac{6000}{ \text{(75 – 20% of 75) }}$ $= \frac{6000 }{(75 – 15) }= \frac{6000 }{60 }$= 100 Shares.

(iii) Nominal Value of Shares = No of Shares×Nominal Value per share = 100 \times 75 = Rs. 7500.

Annual Dividends $= \frac{\text{(Nominal Value of Shares×Rate of Dividend) }}{100}$ $= 7500 \times \frac{25}{100}$= Rs. 1875.

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

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Question 13

Mr. Khanna holds 1600, Rs. 100 shares of a company that pays 12% dividend annually. Calculate his annual dividend. If he had bought these shares at 50% premium, what percentage return does he get on his investment?

Sol :

Nominal Value of Shares = No of Shares×Nominal Value per share = 1600×100 = Rs. 160000.

Cost of Investment in Shares = Nominal Value of Shares + Premium = 160000 + 50% of 160000 = 160000 + 80000 = Rs. 240000.

Annual Dividend $= \frac{\text{Nominal Value of Shares×Rate of Annual Dividend} }{100}$

$= 160000 \times \frac{12}{ 100}$ = Rs. 19200.

Percentage Return on Investment $= \frac{\text{Annual Dividend} \times  100 }{ \text{Cost of Investment}} $ $= 19200 \times \frac{100}{240000 }$= 8%.

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Q14 | Ex-3A | 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 per annum when its Rs. 100 shares can be bought for Rs. 140. Find (i) his annual dividend, (ii) his percentage income on this investment.

Sol :

No of Shares purchased $= \frac{\text{Investment }}{\text{Cost of Investment}} = \frac{11200}{40}$ = 80 shares.

Nominal Value of New Shares = No of Shares×Nominal Value per Share = 80×100 = Rs. 8000.

Annual Dividend $= \frac{\text{Nominal Value of Shares×Rate of Annual Dividend} }{100}$

$= 8000 \times \frac{6}{100}$ = Rs. 480.

Percentage Return on Investment $= \frac{\text{Annual Dividend} \times  100 }{ \text{Cost of Investment}} $ $= \frac{480\times 100}{11200}$ = 4.29%.

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

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Question 15

A company having a capital stock of Rs. 450000 declares a dividend of 4% semi-annually. (i) What is the annual income of a stockholder owning 135 shares at par-value of Rs. 10? (ii) What is the total amount of dividend paid annually by the company?

Sol :

Nominal Value of Shares = No of Shares×Nominal Value per Share = 135×10 = Rs 1350.

Rate of semi-annual dividend = 4% and Rate of Annual Dividend = 8%

(i) Annual Income of Stockholder = Nominal Value of Share×Rate of Annual Dividend $= \frac{1350\times 8}{100}$= Rs. 108.

(ii) Total Amount of Dividend Paid Annually by the Company $= \frac{\text{Capital Stock×Rate of Annual Dividend }}{100} = 450000 \times \frac{8}{100}$

= Rs. 36000.