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S Chand ICSE Maths Solutions Class 10 Chapter 3 Shares and Dividends Exercise 3B

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S Chand ICSE Maths Solutions Class 10 Chapter 3 Shares and Dividends Exercise 3B

Hi students, Welcome to Amans Maths Blogs (AMB). In this post, you will get S Chand ICSE Maths Solutions Class 10 Chapter 3 Shares and Dividends Exercise 3B. This is the chapter of introduction of ‘Shares and Dividends‘ included in ICSE 2020 Class 10 Maths syllabus.

Shares and Dividends Formulas

There are following formulas used to solve the questions of Shares and Dividends:

1. Nominal Value of Shares = No of Shares X Nominal Value per share

2. Premium = No of Shares X Premium per share

3. Cost of Share = Nominal Value of Shares + Premium

4. Discount = No of Shares X Discount per share

5. Cost of Shares = Nominal Value of Share – Discount

6. Cost of Stock = No of Stock X Rate per Stock

7. Annual Dividends on Shares = (Nominal Value of Shares X Rate of Dividend) / 100

8. Sum of money obtained by selling shares = No of Shares X Selling Rate per share

9. No of Share bought = Investment / Market Value per Share

10. Market Price per Share = Cost of Shares / No of Shares.

11. Cost of Share = No of Shares X Market Value per Share

12. Annual Income from Investment = Nominal value of Shares X Rate of Dividends / 100

13. TDS (Tax Deducted at Sources) = Annual Dividend X Rate of Income Tax / 100

14. Amount of Money Invested = No of Shares X Market value per Share

14. Percentage Return on Investment = (Annual Dividend x 100) / Cost of Investment

15. Sale proceeds of n Shares = Nominal value of Shares + 50% Premium

Basic Details of Shares and Dividends

Suppose a company start with a business with an investment of Rs. 1000000. Then,

The total amount invested to start a company is called Capital Stock.

Generally it is not possible for one individual to manage the whole amount. So the total amount is divided into equal parts called Shares.

The shares purchased by an individual is also called Stock.

The persons who buy these shares are called Shareholders or Stockholders.

There are two types of shares known as Common Shares and Preferred Shares.

The common shares are also called Equity Shares.

The profit gained by the company that is distributed among the shareholders is called Dividends. It is calculated on the face value of a share and expressed as percentage.

The preferred shareholders have a first claim on the dividend. When they have been paid, the remaining profit is distributed among the common shareholders.

The original value of a share at which the company sells it to investors and which is printed on the share certificate is called Nominal Value (NV) or Printed Value (PV) of the shares.

The price at which the stock is bought or sold, in the market is called the Market Value (MV) or Cash Value (CV)The market value of a share keeps changing from time to time.

If the market value is more than the face value of the share, the share is called to be above par.

If the market value of a share is the same as its face value, then the share is called to be at par.

If the market value is less than the face value of the share, then the share is called to be below par or at a discount.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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%.

S Chand ICSE Maths Solutions:

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

No of bought Shares = 50 / 1.25 = 40 Shares.

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

Income obtained by Investing = 40 x 8 / 100 = Rs. 3.20.

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

No of bought Shares = 240 / 8 = 30 Shares.

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

Income obtained by Investing = 150 x 9 / 100 = Rs. 13.50.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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?

S Chand ICSE Maths Solutions:

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

Price of the Shares Stand = 360 / 160 = Rs. 2.25

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

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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?

S Chand ICSE Maths Solutions:

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

Price of the Shares Stand = 750 / 600 = Rs. 1.25

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

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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

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

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

The dividend received in cash = ₹ 2,000 x 8/100 = ₹ 160.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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

Dividend received on bought 500 shares = ₹ 400

The rate of dividend received = ₹ 400 x 100 / 5000 = 8%.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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?

S Chand ICSE Maths Solutions:

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

Profit (Dividend) on 1 shares = ₹ 25 x 4 / 100 = Rs. 1.60.

The paying rate = ₹ 1.60 x 100 / ₹ 1.60 = 6.4%.

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

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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?

S Chand ICSE Maths Solutions:

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

No. of bought shares = ₹9,000 / ₹500 = 60 Shares

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

The income obtained by investing = ₹ 6,000 x 6/100 = ₹ 360

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

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

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

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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?

S Chand ICSE Maths Solutions:

Nominal value of shares = Dividend on shares X 100 / Rate of dividend = ₹ 500 X 100/10 = ₹ 5,000

No. of shares purchased = Nominal value of shares / Face Value per share = ₹ 5,000 / 100 = 50 Shares

Cost of 50 shares = ₹ 7,500

Price paid per share to the company = ₹ 7,500 / 50 = ₹ 150.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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

Dividend on shares = Nominal value of shares X Rate of dividend / 100 = 14,000 X 9 / 100 = ₹ 1,260

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

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

Income on investment = ₹ 1,260

Interest on investment = 1,260 x 100/16,800 = = 7 1/2 %.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

Nominal value of shares = Dividend on shares X 100 / Rate of dividend = 720 x 100 / 12 = = ₹ 6,000

No. of shares purchased = Nominal value of shares / Face value per share = 6,000 / 25 = 240 shares

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

Return on investment = Annual income from shares X 100/ Cost of Investment = 720 X 100 / 8,640 = 8.33%

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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

S Chand ICSE Maths Solutions:

(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 = ₹ 9,600 / 48 = 200 shares

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

Annual dividend on shares = Nominal value of shares X Rate of dividend / 100 = 10,000 X 18 / 100 = ₹ 1,800.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

Nominal value of shares = Dividend on shares X 100 / Rate of dividend = ₹ 540 X 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 = Annual dividend on shares X 100 Cost of Investment = 540 X 100 / 4,320 = 12.5%

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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

Annual dividend on shares = Nominal value of shares X Rate of dividend / 100 = 1,80,000 X 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 = Annual dividend on shares X 100 / Cost of Investment = 27,000 X 100 / 2,52,000 = 10.71% = 11% ( to the nearest integer ).

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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

No. of bought shares = ₹ 11,200 / ₹ 140 = 80 Shares

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

∴ The income obtained by investing = ₹ 8,000 X 6 / 100 = ₹ 480

(ii) Rate of return on investment = Annual dividend on shares X 100 / Cost of Investment = 480 X 100 / 11,200 = 4 2/7%.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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

∴ Annual dividend paid by the company = Nominal value of shares X Rate of dividend / 100
= 10,00,000 X 5 / 100 = ₹ 50,000

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

∴ Annual income of a man on 72 shares = Nominal value of shares X Rate of dividend / 100 = 7,200 X 5100 = ₹ 360

(iii) Income on investment at 4% = 7,200 X 4 / 100 = 288

Price paid for each share = Annual dividend on shares X 100 / Income of Investment = 360 X 100 / 288 = ₹ 125.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

(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 = ₹ 1,680 / 26.88 = 62.5 Shares

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

∴ Annual dividend received on shares = Nominal value of shares X Rate of dividend / 100 = 1,500 X 15 / 100 = ₹ 225.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

(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 = ₹ 7,425 / 99 = 75 shares

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

Dividend percentage per share = Annual dividend on shares X 100 / Nominal Value = 1,350 X 100 / 6,750 = 20%.

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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?

S Chand ICSE Maths Solutions:

Let, Abhishek sell X shares. 

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

Face value of X shares = X x ₹ 20 = 20X

Dividend on X shares = 8% of 20X = 20X x 8 / 100 = 8X/5

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

No. of purchased new shares = Sale Proceeds / Rate per new share = 18X/15 = 6X/5

Nominal value of purchased new shares = 6X/5 x 10 = 12X

Dividend on purchased new shares = 12% of 12X = 12X x 12/100 = 36X/25

Change in annual income = ₹ 120

8X/5 − 36X/25 = 120 ⇒ X = 750

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

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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

S Chand ICSE Solutions Class 10 Maths Shares and Dividends Exercise 3B: Ques No 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.

S Chand ICSE Maths Solutions:

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 = X/50 + 9X/250 + 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

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