Concise Mathematics Class 10 ICSE Solutions for Chapter 3 - Shares and Dividend

Exercise 3(A)

1. How much money will be required to buy 400, Rs. 12.50 shares at a premium of Rs. 1?

Ans: Number of shares bought = 400

Rs. 12.50 shares at a premium of Rs. 1me

Nominal value of the share is Rs. 12.50 and market value of the share is:

= Rs. 12.50 +Rs. 1

= Rs. 13.50

Therefore, money required to buy 1 share is Rs. 13.50.

This implies money required to buy 400 shares is:

= 400 x Rs. 13.50

= Rs. 5400

Therefore, money required to buy 400 shares is Rs. 5400.

2. How much money will be required to buy 250, Rs. 15 shares at a discount of Rs. 1.50?

Ans: Number of shares bought = 250

Rs. 15 shares at a discount of Rs. 1.50 me

Nominal value of the share is Rs. 15 and market value of the share is:

= Rs. 15 - Rs 1.50

= Rs. 13.50

Therefore, money required to buy 1 share is Rs. 13.50

This implies money required to buy 250 shares is:

= Rs. 250 x 13.50

= Rs. 3375

Therefore, money required to buy 400 shares is Rs. 3375.

3. A person buys 120 shares at a nominal value of Rs.40 each, which he sells at Rs.42.50 each. Find his profit and profit percent.

Ans: Nominal value of 120 shares is: 

= Rs.40 x 120

=Rs. 4800

Market value of 120 shares is:

= Rs.42.50 x 120

= Rs. 5100

Profit= M.V-N.V

= 5100- 4800

= 300

Profit Percent =  $\dfrac{{Profit}}{{N.V}} \times \;100\% $

=$\;\dfrac{{300}}{{4800}} \times \;100\% $

= $\dfrac{{100}}{{16}}$ 

= 6.25 %

Therefore, profit is Rs. 300 and profit percent is 6.25%.

4. Find the cost of 85 shares of Rs.60 each when quoted at Rs.63.25.

Ans: Market value of 1 share is Rs. 63.25 

Market value of 85 shares is:

= Rs. 63.25 x 85

= Rs. 5376.25

Therefore, the market value of 85 shares is Rs.5376.25.

5. A man invests Rs. 800 in buying Rs. 5 shares and when they are selling at a premium of Rs. 1.15, he sells all the shares. Find his profit and profit percent.

Ans: Nominal value of 1 share is Rs. 5

Market value 1 share is: 

= Rs.5 +Rs.1.15

= Rs.6.15

Total money invested is Rs.800.

Number of shares purchased =$\dfrac{800}{5}$ =160

Market value of 160 shares:

= 160 x Rs.6.15

= Rs. 984

Profit = M.V - N.V 

= Rs.984 - Rs.800

= Rs. 184

Profit percent = $\dfrac{{Profit}}{{N.V}}X\;100\% $

= $\dfrac{{184}}{{800}}X\;100\% $

= 23 %

Therefore, profit is Rs. 184 and profit percent is 23%.

6. Find the annual income derived from 125, Rs.120 shares paying 5% dividend.

Ans: Nominal value of 1 share is Rs. 5

Nominal value of 125 shares is:

= Rs. 120 x 125

= Rs. 15000

Therefore, dividend = 5 % of 15000

= $\dfrac{5}{{100}}\;X\;15000$

= Rs. 750

7. A man invests Rs.3,072 in a company paying 5% per annum, when it's Rs.10 share can be bought for Rs.16 each. Find:

(i) His Annual Income;

Ans: (i) Nominal value of 1 share is Rs. 10

Market value 1 share is Rs. 16 

Total money invested is Rs. 3072.

Number of shares purchased = $\dfrac{{3072}}{{16}} = \;192$

Nominal value of 192 shares:

= 192 x Rs.10 

= Rs. 1920

So, Annual Income = 5% of  Rs.1920 

= $\dfrac{5}{{100}}\;X\;1920\;$

= Rs. 96

Therefore, income is Rs.96.

(ii) His Percentage Income on his Investment.

Ans: (ii) So, Income % = $\dfrac{{96}}{{3072}}X\;100\% $

= 3.125%

= 3$\dfrac{1}{8}\% $

Therefore, income percent is 3$\dfrac{1}{8}\% .$

8. A man invests Rs.7,770 in a company paying 5 percent dividend when a share of nominal value of Rs.100 sells at a premium of Rs.5. Find:

(i) The Number of Shares Bought;

Ans: (i) Nominal value of 1 share is Rs. 100

Market value 1 share is: 

= Rs. 100 + Rs. 5

= Rs. 105

Total money invested is Rs.7770.

Number of shares purchased= $\dfrac{{7770}}{{105}} = 74.$

(ii) Annual Income

Ans: Nominal value of 74 shares is:

= 74 x Rs. 100

= Rs. 7400

So, Annual Income = 5% of Rs 7400

= $\dfrac{5}{{100}}X\;7400$

= Rs. 370

Therefore, income is Rs.370.

(iii) Percentage income.

Ans: So, Income % = $\dfrac{{370}}{{7770}}X\;100\% $

= 4.76 %

Therefore, income percent is 4.76%.

9. A man buys Rs.50 shares of a company, paying 12 percent dividend, at a premium of Rs. 10. Find:

(i) The Market Value of 320 Shares;

Ans: Nominal value of 1 share is Rs. 50

Market value 1 share is: 

= Rs. 50 +Rs. 10

= Rs. 60

Market value of 320 shares is:

= Rs. 60 x 320 

= Rs.19200

Therefore, Market value of 320 shares is Rs. 19200.

(ii) His Annual Income;

Ans: Nominal value of 320 shares is: 

= Rs. 50 X 320

= Rs. 16000

So, Annual Income= 12% of Rs16000

= $\dfrac{{12}}{{100}}X\;16000$

= Rs. 1920

Therefore, income is Rs. 1920.

(iii) His profit percent.

Ans: So, Profit % = $\dfrac{{1920}}{{19200}}X\;100\% $

= 10 %

Therefore, profit percent is 10%.

10. A man buys Rs.75 shares at a discount of Rs.15 of a company paying 20 % dividend. Find

(i) The Market Value of 12 Shares;

Ans: Nominal value of 1 share is Rs. 75

Market value 1 share is: 

= Rs.75 - Rs.15

= Rs. 60

Market value of 120 shares is:

= Rs.60 x 120

= Rs. 7200

Therefore, Market value of 120 shares is Rs.7200.

(ii) His Annual Income;

Ans: Nominal value of 120 shares is: 

= 75 x 120

= 9000

So, Annual Income = 20% of Rs. 9000

= $\dfrac{{20}}{{100}}$X 9000

= Rs. 1800

Therefore, income is Rs. 1800.

(iii) His Profit Percent.

Ans: So, Profit % = $\dfrac{{1800}}{{7200}}X\;100\% $ 

= 25%

Therefore, profit percent is 25%.

11. A man has 300, Rs.50 shares of a company paying 20 % dividend. Find his net income after paying 3% income tax.

Ans: Nominal value of 1 share is Rs. 50.

Nominal value of 300 shares is:

= 300 X Rs. 50

= Rs.15000  

Therefore, Dividend: 

= 20% of   Rs. 15,000

= $\dfrac{{20}}{{100}}X\;$Rs. 15,000

= Rs. 3000 

Income tax paid 

= 3% of Rs. 3000

= $\dfrac{{30}}{{100}}{\text{X}}\;$Rs. 3,000

= Rs. 90

Net income:

= Rs. 3000 - Rs. 90

= Rs. 2910

Therefore, his net income is Rs. 2910.

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

Ans: Nominal value of 1 share is Rs. 10. 

Nominal value of 1000 shares is:

= 1000 X 10

= Rs. 10000

Therefore, Dividend:

= 15% of Rs 10,000

= $\dfrac{{15}}{{100}}X\;$Rs. 10,000

= Rs. 1500

Income tax paid

= 22% of Rs. 1500

= $\dfrac{{22}}{{100}}X\;$Rs. 1500

= Rs. 330

Net income:

= Rs. 1500 - C 330

= Rs. 1170

Therefore, his net income is Rs. 2910.

13. A man invests Rs. 8800 in buying shares of a company of face value of rupees hundred each at a premium of 1 0%. If he earns Rs.1200 at the end of the year as dividend, find:

(i) The Number of Shares he Has in the Company

Ans: Total investment is Rs. 8800.

Nominal value of 1 share is Rs. 100

Market value of 1 share is Rs. 110.

Number of shares purchased is:

= $\dfrac{{8800}}{{110}}$

= 80

Therefore, the number of shares purchased is 80.

(ii) The Dividend Percent Per Share.

Ans: Nominal value of 80 shares is:

= 80 X Rs. 100

= Rs. 8000

Let the dividend be y%.

y% of Rs. 8000 = Rs.1200

$\dfrac{{\text{y}}}{{100}}{\text{X}}$Rs. 8,000 = Rs.1200

y = $\dfrac{{1200}}{{80}}$ 

y   = 15%

Therefore, the dividend is 15%.  

14. A man invests Rs.1680 in buying shares of nominal value Rs.24 and selling at 12% premium. The dividend on the shares is a 12 % premium. The dividend on the shares is 15% per annum. Calculate

(i) The Number of Shares he Buys;

Ans: Total investment is Rs. 1680.

Nominal value of 1 share is Rs. 24

Market value of 1 share is: 

= Rs. 24+ 12% of Rs. 24

= Rs. 24 + $\dfrac{{12}}{{100}}X\;$Rs. 24

= Rs. 24 + Rs. 2.88

= Rs. 26.88

Number of shares purchased is:

= $\dfrac{{1680}}{{26.88}}$

= 62.5

Therefore, the number of shares purchased is 62.5.

(ii) The Dividend he Receives Annually.

Ans: Nominal value of 62.5 shares is: 

= 62.5 X Rs. 24

= Rs. 1500

Dividend = 15% of Rs. 1500

= $\dfrac{{15}}{{100}} \times $Rs. 1500

= Rs. 225 

Therefore, the dividend is Rs. 225.  

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

Ans: Total investment is Rs. 7500.

Nominal value of 1 share is Rs. 100

Let the number of shares purchased be y.

Nominal value of y share is:

= Rs. 100 x y

= Rs. 100 y

Dividend percent = 10%

Dividend = Rs. 500  

10% of Rs. 100 y = Rs. 500

$\dfrac{{10}}{{100}}{\text{X}}\;$Rs. 100 y = Rs. 500

10 y = 500 

y = 50 shares

Therefore, market value of 1 share is: 

$ = \dfrac{{7500}}{{50}}$

= Rs. 150

Therefore, Rs. 150 is paid for each share.

Exercise 3(B)

1. A man buys 75, Rs. 100 shares paying 9 percent dividend. He buys shares at such a price that he gets 12 percent of his money. At what price did he buy the shares?

Ans: Nominal value of 1 share is Rs. 100

Nominal value of 75 shares is:

= Rs. 100 X 75 

= Rs. 7500

Dividend = 9% of Rs. 7500

= $\dfrac{9}{{100}} \times \;7500$

= Rs. 675

Let the market price of 1 share be Rs. y.

The market price of 75 shares is Rs. 75 y.

Profit% on investment = 12%

12% of 75 y = Rs. 675

$\dfrac{{12}}{{100}} \times 75y = 675$

y = $\dfrac{{9\; \times \;100}}{{12}}$

y = Rs. 75

Therefore, money required to buy 75 shares is Rs.75. 

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

Ans: Nominal value of 1 share is Rs. 25

Market value 1 share is Rs. 40.

Profit on investment = 4%

Profit on 1 share:

= 4% of Rs. 40

= $\dfrac{4}{{100}} \times 40$

= Rs. 1.60

Dividend% = $\dfrac{{1.60}}{{25}} \times 100$

= 6.4%

Dividend on 60 shares:

= 60 \[ \times \] Rs. 1.60

= Rs. 96

Therefore, the rate percent paid by the company is 6.4%and the dividend on buying 60 shares is Rs. 96.

3. Hundred rupee shares of a company are available in the market at a premium of Rs.20. Find the rate of dividend given by the company when a man’s return on his investment is 15 percent.

Ans: Nominal value of 1 share is Rs. 100 

Market value 1 share: 

= Rs. 100+ Rs. 20

= Rs. 120

Profit on investment = 15% 

Profit on 1 share:

= 15% of Rs. 120

= $\dfrac{{15}}{{100}} \times 120$

= Rs. 18 

Dividend% =$\dfrac{{18}}{{100}} \times \;100$

= 18%

Therefore, the rate percent paid by the company is 18%.

4. Rs.50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20 percent.

Ans:

Nominal value of 1 share is Rs. 50  

Market value 1 share:

= Rs. 50 - 10% of Rs. 50 

= Rs. 50 - Rs. 5

= Rs. 45  

Profit on investment = 20%

Profit on 1 share: 

= 20% of Rs. 45 

= $\dfrac{{20}}{{100}} \times 45\;$

= Rs. 9

Dividend % = $\dfrac{9}{{50}} \times 100\;$

= 18%

Therefore, the rate percent paid by the company is 18%.

5. A company declares an 8 percent dividend to the shareholders. If a man receives Rs.2,840 as his dividend, find the nominal value of his shares?

Ans: Dividend percent = 8%

Dividend = Rs. 2840

Let the nominal value be Rs. x. 

8% of x = Rs. 2840

$\dfrac{8}{{100}} \times x = 2840$

x = Rs. 35500

Therefore, the nominal value of the shares is Rs.35500.

6. How much should a man invest in Rs.100 shares selling at Rs.110 to obtain an annual income of Rs.1,680, if the dividend declared is 12%?

Ans: Nominal value of 1 share is Rs. 100

Market value 1 share is Rs. 110

Let the number of shares purchased is n.

Nominal value of n shares is Rs100 n.

Dividend percent =12%

Dividend = Rs. 1680

So, 12 % of 100 n = Rs. 1680

$\dfrac{{12}}{{100}} \times 100n = 1680$

n = $\dfrac{{1680}}{{12}}$ 

n = 140 

So, market value of 140 shares is: 

= 140 x Rs. 110

= Rs. 15400

Therefore, the market value of 140 shares is Rs.15400.  

7. A company declares a dividend of 11.2% to all its shareholders. If it's Rs. 60 share is available in the market at a premium of 25%, how much should Rakesh invest in buying the shares of this company, in order to have an annual income of Rs.1,680?

Ans: Nominal value of 1 share is Rs. 60

Market value 1 share:

= Rs. 60 + 25% of Rs. 60 

= Rs. 60 + $\dfrac{{25}}{{100}} \times \;60\;$

= Rs. 60 + Rs. 15

= Rs. 75

Let number of shares purchased is n

Nominal value of n shares is Rs60n.

Dividend percent = 11.2%

Dividend = Rs. 1680

So,

11.2 % of 60 n = Rs. 1680

$\dfrac{{11.2}}{{100\;}} \times 60\;n\; = \;1680$

n = $\dfrac{{1680\; \times 100}}{{11.2\; \times 60\;}}$ 

n = 250 

So, Market value of 250 shares is:

= 250 $ \times $ 75

= Rs. 18570

Therefore, the market value of 250 shares is Rs. 18570.

8. A man buys 400, twenty-rupee shares at a premium of Rs.4 each and receives a dividend of 12 %. Find:

(i) The Amount Invested by Him.

Ans: No. of shares purchased= 400

Nominal value of 1 share is Rs. 20

Market value 1 share is:

=Rs. 20 + Rs. 4

= Rs. 24 

Nominal value of 400 shares is:

= 400 $ \times $ Rs. 20

= Rs. 8000

Market value of 400 shares is:

= 400 X Rs. 24

= Rs. 9600

Therefore, total money invested by him is Rs.9600. 

(ii) His Total Income From the Shares.

Ans: Dividend percent =12% 

Dividend = 12% of Rs. 8000

= $\dfrac{{12}}{{100\;}} \times 8000$

= Rs. 960 

Therefore, his total income from the shares is Rs. 960.

(iii) Percentage Return on His Money.

Ans: So, percentage return= $\dfrac{{Income\;}}{{Investment}} \times 100\;\% $ = $\dfrac{{960\;}}{{9600}}\; \times 100\;\% $ = 10 %

Therefore, the percentage return on his money is 10%.

9. A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12 % on his money. Calculate:

(i) The Amount Invested by Him.

Ans: No. of shares purchased= 400

Nominal value of 1 share is Rs. 20

Market value 1 share is: 

= Rs. 20 - 20% of Rs. 20

= Rs. 20 - $\dfrac{{20}}{{100}}\; \times \,20$

= Rs. 20 - Rs. 4 

= Rs. 16

Nominal value of 400 shares is: 

= Rs. 400 x 20 

= Rs. 8000

Market value of 400 shares is:

= Rs. 400 x 16 

= Rs. 6400

Therefore, total money invested by him is Rs. 6400.

(ii) The Rate of Dividend Paid by the Company.

Ans: Return percent = 12%

Income = 12 % of Rs. 6400 = $\dfrac{{12}}{{100}} \times 6400$ = Rs. 768

So, Dividend% = $\dfrac{{Income}}{{Nominal\;Value}}$ = $\dfrac{{768}}{{8000}} \times 100\% $ = 9.6%

Therefore, the rate of dividend paid by the company is 9.6%.

10. A company, with 10,000 shares of Rs. 100 each, declares an annual dividend of 5%.

(i) What is the Total Amount of Dividend Paid by the Company?

Ans: Nominal value of 1 share = Rs. 100

Nominal value of 10,000 shares: 

= 10000 x Rs. 100

= Rs. 10, 00, 000

Dividend% = 5 %

Dividend = 5 % of Rs. 10, 00, 000 = $\dfrac{5}{{100}} \times 10,00,000$ = Rs. 50,000

Therefore, the total amount of dividend paid by the company is Rs. 50,000. 

(ii) What Should be the Annual Income of a Man Who has 72 Shares in the Company?

Ans: Nominal value of 72 shares is:

= Rs. 100 x 72

= Rs. 7200

Dividend = 5% of Rs. 7200

= $\dfrac{5}{{100}} \times 7200$

= Rs. 360

(iii) If He Received Only 4% of his Investment, Find the Price he Paid for Each Share.

Ans: Let the market value of 1 share is Rs. 100.

Then market value of 10,000 shares = Rs. 10000 y

Return% = 4%

4 % of Rs. 10000 y = Rs. 50000

$\dfrac{4}{{100}}\; \times 10000\;y\; = \;50000$

 y = $\dfrac{{50000}}{{400}}$  

y = Rs. 125

Therefore, the market value of 1 share is Rs. 125. 

11. A lady holds 1800, Rs.100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what is the return she gets as percent on her investment? Give your answer to the nearest integer.

Ans: Nominal value of 1 share is Rs. 100.

Market value of 1 share = Rs. 100 + 40% of Rs. 100

= Rs. 100 + $\dfrac{{40}}{{100}} \times 100$

= Rs. 100 + Rs. 40 

= Rs. 140

No. of shares purchased = 1800

Nominal value of 1800 shares 

= 1800 x Rs. 100

= Rs. 180000 

Market value of 1800 shares

= 1800 x Rs. 100

= Rs. 180000

Market value of 1800 shares

= 1800 x Rs. 140

= Rs. 252000

Dividend % = 15%

Dividend = 15% of Rs. 180000

= $\dfrac{{15}}{{100}} \times 180000$

= Rs. 27000

So, return % = \[\dfrac{{{\text{Income}}}}{{{\text{Investment}}}} \times {\text{100\% }}\]

= $\dfrac{{27000\;}}{{252000}}\; \times 100\% $

= 10.7%

= 11 %

Therefore, the return percentage is 11%. 

12. A man invests Rs.11,200 in a company paying 6% per annum when its Rs.100 shares can be bought for Rs.140. Find:

(i) His Annual Dividend

Ans: Nominal value of 1 share is Rs. 100

Market value of 1 share is Rs. 140.

Total investment = Rs.11200

Number of shares purchased:

= $\dfrac{{11200}}{{400}}$

= 80 shares

Then nominal value of 80 shares is:

= 80 x 100

= Rs. 8000

Dividend% = 15%

Dividend: = 6% of Rs. 8000

= \[\dfrac{6}{{100}}X\;8000\] 

= Rs. 480   

(ii) His Percentage Return on His Investment.

Ans:  So, return % = $\dfrac{{Income}}{{Investment\;}} \times 100\% $

= $\dfrac{{480}}{{11200}} \times 100\% $   

= 4.29%

Therefore, the return percentage is 4.29%.  

13. Mr. Sharma has 60 shares of N.V Rs.100 and sells them when they are at a premium of 60%. He invests the proceeds in shares of nominal value Rs.50, quoted at 4% discount, and pays an 18% dividend annually. Calculate:

(i) The Sale Proceeds;

Ans: Nominal value of 1 share is Rs. 100

Nominal value of 60 shares is:

= 60 x 100

= Rs. 6000

Market value of 1 share is:

= Rs. 100 + 60% of Rs. 100

= Rs. 100 + $\dfrac{{60}}{{100}} \times 100$ 

= Rs. 100 + Rs. 60

= Rs. 160

Market value of 60 shares is:

= 60 $ \times $ 160

= Rs. 9600

Therefore, the market value of 60 shares is Rs. 9600.

(ii) The Number of Shares He Buys;

Ans: Nominal value of 1 share is Rs. 50

Market value of 1 share is:

= Rs. 50 - 4% of Rs.50

= Rs. 50 - $\dfrac{4}{{100}} \times 50$

= Rs. 50 - Rs.2

= Rs. 48

Number of shares purchased is: 

= $\dfrac{{9600}}{{48}}$

= 200 shares

Therefore, the number of shares purchased is 200.

(iii) His Annual Dividend From the Shares.

Ans: Dividend% = 18%

Dividend:

= 18% of Rs. 10000

= $\dfrac{{18}}{{100}} \times 10000$

= Rs. 1800

Therefore, annual dividend from the share is Rs. 1800.

14. A company with 10,000 shares of nominal value Rs.100 declares an annual dividend of 8% to the shareholders.

(i) Calculate the total amount of dividend paid by the company.

Ans: Nominal value of 1 share = Rs. 100

Nominal value of 10,000shares:

= 10000 X Rs. 100

= Rs. 10, 00, 000

Dividend% = 8% 

Dividend = 8% of Rs. 10, 00, 000

=$\dfrac{8}{{100}} \times $ Rs. 10, 00, 000

= Rs. 80,000

Therefore, the total amount of dividend paid by the company is Rs. 80,000. 

(ii) Ramesh had bought 90 shares of the company at Rs.150 per share. Calculate the dividend he receives and the percentage of return on his investment.

Ans:  Market value of 90 shares is:

= 90 X Rs. 150

= Rs. 13500

Nominal value of 90 shares is: 

= 90 X Rs. 100

= Rs. 9000

Dividend: 

= 8% of Rs. 9000

= $\dfrac{8}{{100}} \times 9000$

= Rs. 720

So, return % = $\dfrac{{Income}}{{Investment\;}} \times 100\% $

= $\dfrac{{720}}{{13500}} \times 100\% $

= 5$\dfrac{1}{3}$ %

Therefore, the return percentage is 5$\dfrac{1}{3}$ %.

15. Which is the better investment: 16% Rs.100 shares at 80 or 20% Rs.100 shares at 120?

Ans: 1st case

Market value of 1 share is Rs. 80

Nominal value of 1 share is Rs. 100

Dividend = 16%

Income on Rs. 80:

= 16% of Rs. 100 

= $\dfrac{{16}}{{100}} \times $100 

= Rs. 16

Income on Rs. 1: 

= $\dfrac{{16}}{{80}}$

= Rs. 0.20

2nd case

Market value of 1 share is Rs. 120

Nominal value of 1 share is Rs. 100

Dividend = 20 %

Income on Rs. 120

= 20% of Rs. 100

= $\dfrac{{20}}{{100}} \times $ 100 

= Rs. 20 

Income on Rs. 1:

= $\dfrac{{20}}{{120}}$

= Rs. 0.17

Therefore, 16% Rs. 100 shares at 80 is a better investment.

16. A man has a choice to invest in hundred-rupee shares of two firms at Rs.120 or at Rs.132. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum. Find: 

(i) which Company is Giving a Better Return.

Ans: 1st firm 

Market value of 1 share is Rs. 120

Nominal value of 1 share is Rs. 100

Dividend= 5%

Income on Rs. 120:

= 5% of Rs. 100 

= $\dfrac{5}{{100}} \times 100$

= Rs. 5 

Income on Re1:

= $\dfrac{5}{{120}}$

= Rs. 0.041

2nd firm

Market value of 1 share is Rs132

Nominal value of 1 share is Rs. 100

Dividend= 6%

Income on Rs. 132:

= 6% of Rs. 100 

= $\dfrac{6}{{100}} \times 100$

= Rs. 6

Income on Re1:

= $\dfrac{6}{{132}}$

= Rs. 0.045

Therefore, investment in a second firm is giving a better return.

(ii) If a Man Invests  Rs.26,400 with each firm, how much will be the difference between the annual return from the two firms?

Ans: Income on investment in first firm

= $\dfrac{5}{{120}} \times 26400$

= Rs. 1100

Income on investment in second firm

= $\dfrac{6}{{132}} \times 26400$

= Rs. 1200

So, difference in both the returns

= Rs. 1200 - Rs. 1100

= Rs. 100

Therefore, the difference in both the returns is Rs. 100.

17. A man bought 360, ten- rupee shares of a company, paying 12 percent per annum. He sold the shares when their price rose to Rs.21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at Rs.3.50 per share. Find the annual change in his income.

Ans: 1st case

Nominal value of 1 share is Rs. 10

Market value of 1 share is Rs. 21

Nominal value of 360 shares:

= 360 x Rs. 10

= Rs. 3600

Market value of 360 shares is:

= 360 x Rs. 21

= Rs. 7560

Dividend percent = 12%

Dividend = 12% of Rs. 3600

= $\dfrac{{12}}{{100}} \times 3600$

= Rs. 432

2nd case

Nominal value of 1 share is Rs. 5

Market value of 1 share is Rs. 3.50

Number of shares purchased = $\dfrac{{7560}}{{3.50}}$= 2160 shares 

Nominal value of 2160 shares:

= 2160 x Rs. 5

= Rs. 10800 

Dividend percent = 4.5%

Dividend= 4.5% of Rs. 10800 

= \[\dfrac{{4.5}}{{100}} \times 10800\]

= Rs. 486

Annual change in income:

= Rs. 486 - Rs. 432

= Rs. 54

Therefore, there is an increase of Rs. 54 in annual income.

18. A man sold 400 (Rs.20) shares of a company, paying 5% at Rs. 18 and invested the proceeds in (Rs.10) shares of another company paying 7% at Rs. 12. How many (Rs.10) shares did him buy and what was the change in his income?

Ans: 1st case 

Nominal value of 1 share is Rs. 20

Market value of 1 share is Rs. 18

Nominal value of 400 shares:

= 400 $ \times $ Rs. 20

= Rs. 8000

Market value of 400 shares is:

= 400 $ \times $ Rs. 18

= Rs. 7200

Dividend percent = 5%

Dividend = 5% of Rs. 8000

= $\dfrac{5}{{100}} \times 8000$

= Rs. 400

2nd case

Nominal value of 1 share is Rs. 10

Market value of 1 share is Rs. 12 

Number of shares purchased

= $\dfrac{{7200}}{{12}}$

= 600 shares

Nominal value of 600 shares:

= 600 $ \times $ Rs. 10

= Rs. 6000

Dividend percent = 7%

Dividend = 7% of Rs. 6000  

= $\dfrac{7}{{100}} \times 6000$

= Rs. 420

Annual change in income:

= Rs. 420 - Rs. 400

= Rs. 20

Therefore, there is an increase of Rs. 20 in annual income.

19. Two brothers A and B invested Rs.16,000 each in buying shares of two companies. A buys 3% hundred-rupee shares at 80 and B buys ten-rupee shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B. 

Ans: For A

Total investment is Rs. 16000

Nominal value of 1 share is Rs. 100

Market value of 1 share is Rs. 80

Number of shares purchased = $\dfrac{{16000}}{{80}}$

= 200 shares

Nominal value of 200 shares:

= 200 X Rs. 100

= Rs. 20000

Dividend percent is 3%.

Dividend = 3% of Rs20000

= $\dfrac{3}{{100}} \times 20000$  

= Rs. 600

For B

Total investment is Rs. 16000.

Nominal value of 1 share is Rs. 10

Market value of 1 share is Rs. 10 

Number of shares purchased = $\dfrac{{16000}}{{10}} = \;1600$ shares

Nominal value of 1600 shares:

= 1600 $ \times $ Rs. 10

= Rs. 16000

Dividend received by B is equal to the dividend received by A. 

Dividend = $\dfrac{{600}}{{16000}} \times 100$

= 3.75 %

Therefore, the rate of dividend received by B is 3.75%.

20. A man invests Rs.20,000 in buying shares of N.V Rs.26 at 10% premium. The dividend on the shares is 15% per annum. Calculate:

(i) The Number of Shares He Buys.

Ans: Total investment is Rs. 16000. 

Nominal value of 1 share is Rs. 10

Market value of 1 share is:

= Rs26 + 10% of Rs. 26

= Rs. 26 + $\dfrac{{10}}{{100}} \times 26$

= Rs. 26 + Rs. 2.6

= Rs. 28.6 

Number of shares purchased = $\dfrac{{20020}}{{28.60}} = \;700\;shares$

(ii) The Dividend he Receives Annually.

Ans: Nominal value of 700 shares:

= 700 x Rs. 26

= Rs. 18200

Dividend percent = 15%

Dividend = 15% of Rs. 18200 

= $\dfrac{{15}}{{100}} \times 18200$

= Rs. 2730

(iii) The Rate of Interest he Gets on his Money.

Ans: So, Income % = $\dfrac{{Income}}{{Investment}} \times 100\% $

= $\dfrac{{2730}}{{20020}} \times 100\% $

= $\dfrac{{150}}{{11}}\% $

= 13 $\dfrac{7}{{11}}$%

Therefore, the rate of interest he gets on his money is 13 $\dfrac{7}{{11}}$%.                                    

Exercise 3(C)

1. By investing Rs. 45,000 in 10% Rs. 100 shares, Sharad gets Rs. 3,000 as dividend .Find the market value of each share.

Ans: Annual income from 1 share= 10% of Rs. 100

= $\dfrac{{10}}{{100}}$ $ \times $ 100

= Rs. 10

Total annual income = Rs. 3000

Number of shares bought = $\dfrac{{Total\;annual\;income\;}}{{Annual\;income\;from\;1\;share}}$

= $\dfrac{{3000}}{{10}}$

= 300

Market value of 1share = $\dfrac{{Total\;investment\;}}{{No.of\;shares}}$

= $\dfrac{{45000}}{{300}}$

= Rs. 150

2. Mrs. Kulkarni invests Rs. 1.31,040 in buying Rs. 100 shares at a discount of 9%.She sells shares worth Rs. 72,000 at a premium of 10% and rest at a discount of 5%.Find her total gain or loss on the whole.    

Ans: Investment = Rs. 131040

N.V. of 1 share = Rs. 100

Discount= 9% of Rs. 100

= $\dfrac{9}{{100}}\,x\;100$

= Rs. 9

M.V. of 1 share = Rs. 100 – Rs. 9 = Rs. 91 

Number of share purchased = $\dfrac{{Investment\;\;}}{{M.V\;of\;1\;share}}$

= $\dfrac{{131040}}{{91}}$

= 1440

Number of shares worth Rs. 72,000 = $\dfrac{{72000}}{{100}} = \;720$

Mrs. Kulkarni sells 720 shares at a premium of 10%

M.V. of 1 share = Rs. 100 + Rs. 10 = Rs. 110

Selling price of 720 shares = 720 $ \times $ Rs. 110

= Rs. 79200

Number of remaining shares = 1440 - 720

= 720

She sells 720 shares at a discount of 5%

M.V. of 1 share = Rs. 100 - Rs. 5 = Rs. 95

Selling price of 720 shares = 720 x Rs. 95 = Rs. 68400 

Total selling price = Rs. 79200 + Rs. 68400

= Rs. 147600

Total gain = Total selling price - investment

= Rs. 147600 - Rs. 131040

= Rs. 16560

3. A man invested a certain sum in buying 15% Rs. 100 shares at 20% premium. Find:

(i) His Income from One Share

Ans: Dividend on 1 share = 15% of Rs. 100

= $\dfrac{{15}}{{100}} \times 100\;$

= Rs. 15

So, the income of 1 share is Rs. 15. 

(ii) The Number of Shares Bought to Have an Income from Dividend Rs. 6480.

Ans: Number of shares bought by man = $\dfrac{{annual\;income}}{{dividend\;on\;one\;share}}$ 

= $\dfrac{{6480}}{{15}}\;$ = Rs. 432

(iii) Sum Invested.

Ans: Since the man bought shares of Rs. 100 at 20% premium,

Market value of one share = Rs. $\;\left( {1 + \dfrac{{20}}{{100}}} \right) \times 100$

= Rs. $\;\left( {\dfrac{{20}}{{100}}} \right) \times 100$  

= Rs. 120

Total investment = (Number of shares X total investment market value of 1 share)\

= 432 $ \times $ Rs. 120

= Rs. 51,480 

5. Gagan invested 80% of his savings in 10% Rs. 100 shares at 20% premium and the rest of his savings at 20% discount. If his incomes from these shares is Rs. 5600, calculate:

(i) His Investment in Shares on the Whole.

Ans: Let the total investments be Rs. x

For 1st part:

N.V. of each share = Rs. 100

M.V. of each share = Rs. $\left( {100 + \dfrac{{20}}{{100}} \times 100} \right)$

= Rs. 120

Number of shares bought = $\dfrac{{0.8\;x\;}}{{120}}$

Dividend on each share = 10% of Rs. 100

= Rs. $\dfrac{{10}}{{100}}\, \times \;100$

= Rs. 10

Total dividend = Rs. 10 x $\dfrac{{0.8\;x\;}}{{120}}$ = Rs. $\dfrac{{0.8\;x\;}}{{12}}$

For 2nd part:

N.V. of each share =Rs. 50 

M.V. of each share = Rs. $\left( {50 - \dfrac{{20}}{{100}} \times 50} \right)$

= Rs. 40

Number of shares bought = $\dfrac{{0.2\;x\;}}{{40}}$

Dividend on each share = 20% of Rs. 50 

= Rs. $\dfrac{{20}}{{100}} \times 50$

= Rs. 10

Total dividend = Rs. 10 x $\dfrac{{0.2\;x\;}}{{40}}$ = Rs. $\dfrac{{0.2\;x\;}}{4}$

Given that dividends from both the investments is Rs. 5600

Rs. $\dfrac{{0.8\;x\;}}{{12}}$ + Rs. $\dfrac{{0.2\;x\;}}{4}$ = 5600

$\dfrac{{0.8\;x\; + \;0.6\;x\;}}{{12}} = \;5600$

x = $\dfrac{{5600\; \times 12}}{{1.4}} = \;48,000$ 

Thus, his investment in shares on the whole is Rs. 48,000.

(ii) The Number of Shares of the First Kind that he Bought.

Ans: Number of shares bought of first kind = $\dfrac{{0.8\;x\;}}{{120}}$

= $\dfrac{{0.8 \times 48000\;}}{{120}}$

= Rs. 320

(iii) Percentage Return, on the Shares Bought, on the Whole.

Ans: Total dividend (return) = Rs. $\dfrac{{0.8\;x\;}}{{12}}$ + Rs. $\dfrac{{0.2\;x\;}}{4}$

= Rs. $\dfrac{{0.8 \times 48,000\;}}{{12}}$ + Rs. $\dfrac{{0.2 \times 48,000\;}}{4}$

= Rs. 5600

Percentage return = $\dfrac{{5600}}{{48000}} \times \;100$

= 11$\dfrac{2}{3}\% $

6. Aishwarya bought 496, Rs. 100 shares at Rs. 132 each. Find:

(i) Investment made by her.

Ans: N.V. of each share = Rs. 100

M.V. of each share = Rs. 132

Investment made by her

= 496 $ \times $ Rs. 132 

= Rs. 65,472

(ii) Income of Aishwarya from these shares, if the rate of dividend is 7.5%.

Ans: Dividend on 1 share 

= 7.5% of Rs. 100

= Rs. $\left( {\dfrac{{7.5}}{{100}} \times 100} \right)$

= Rs. 7.5      

Income of Aishwarya 

= 496 $ \times $ Rs. 7.5

= Rs. 3,720 

(iii) How much extra must Aishwarya invest in order to increase her income by Rs. 7200?

Ans: If she wants to increase her income by Rs. 7,200,

The number of shares she should buy

= $\dfrac{{increase\;in\;the\;income}}{{income\;of\;one\;share}}$

= $\dfrac{{7,200}}{{7.5}}$

= 960

So, she should invest = 960 $ \times $ Rs. 132

= Rs. 1, 26, 720

7. Gopal has some Rs. 100 shares of the comanyA, paying 10% dividend. He sells a certain number of these shares at a discount of 20% and invests the proceeds in Rs. 100 shares at Rs. 60 of company B paying 20% dividend. If his income, from the share sold, increases by Rs. 18,000, find the number of shares sold by Gopal.

Ans: Let the number of shares the man sold be x.

N.V. of share = Rs. 100

Rate of dividend = 10%

Dividend on each share = 10% of Rs. 100 

= Rs. $\left( {\dfrac{{10}}{{100}} \times 100} \right)$

= Rs. 10

So, dividend on shares = Rs. 10 x 

Selling price of each share = Rs. 100 - 20% of Rs. 100

= Rs. 100 - Rs. $\left( {\dfrac{{20}}{{100}} \times 100} \right)$

= Rs. 80

Selling price of shares = Rs. 80 x 

The proceeds he invested in Rs. 100 shares at Rs. 60 of company B paying 20% dividend.

N.V. of share = Rs. 100

M.V. of share = Rs. 60

Number of shares bought = $\dfrac{{Amount\;invested}}{{M.V.\;of\;each\;share}}$

= $\dfrac{{80x}}{{60}}$

= $\dfrac{{4x}}{3}$

Dividend on each share = 20% of Rs. 100

= $\dfrac{{20}}{{100\;}} \times 100$

= Rs. 20     

Total dividend received = (Dividend on each other X number of shares) = 20 $ \times $ $\dfrac{{4x}}{3}$

= $\dfrac{{80x}}{3}$

Increase in the income = 18,000

$\dfrac{{80x}}{3} - 10x\; = \;18,000$

$\dfrac{{50x}}{3} = \;18,000$ 

x = Rs. 1,080 

Hence, the number of shares sold by Gopal is Rs. 1,080.

8. A man invests a certain sum of money in 6% hundred-rupee shares at Rs. 12 premium. When the shares fell to Rs. 96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at Rs. 8. If the change in his income is Rs. 540, find the sum invested originally.

Ans: Let the original sum invested be x.

N.V. value of 1 share = Rs. 100

M.V. value of 1 share = Rs. 100 + Rs. 12

= Rs. 112

Number of shares purchased = $\dfrac{x}{{112}}$

Income on 1 share at 6% = Rs. 6 

Total income = (Number of shares X income on 1 share)

= $\dfrac{x}{{112}} \times $ 6 = Rs. $\dfrac{{3x}}{{56}}$

Proceeds from sale of original shares at Rs. 96 per share

= Number of shares x Rs. 96

= $\dfrac{x}{{112}} \times $ 96 

= Rs. $\dfrac{{6\;x}}{7}\;$

Number of Rs. 10 shares purchased at Rs. 8 per share from proceeds of original shares

= $\dfrac{{proceeds\;from\;sale\;of\;original\;shares}}{8}$

= $\dfrac{{\dfrac{{6\;x}}{7}}}{8}$

= Rs. $\;\dfrac{{3\;x}}{{28}}$

Income per new share of Rs. 10 at 10% = Rs. $\left( {\dfrac{{10}}{{100}} \times 10} \right)$

= Rs. 1

Total income from new shares = (number of shares X income per share) = Rs. $\dfrac{{3\;x}}{{28}}$ $ \times $ 1

= Rs. $\dfrac{{3\;x}}{{28}}$ 

Given change in income = Rs. 540

Income from old shares - income from new shares = 540

540 = $\;\dfrac{{3\;x}}{{28}}$ -$\;\dfrac{{3\;x}}{{56}}$ 

540 = $\dfrac{{3\;x}}{{56}}$ 

x = $\dfrac{{540\; \times 56}}{3}$   

x = Rs. 10,080

Thus, the original sum invested is Rs. 10,080.

9. Mr. Gupta has a choice to invest in ten -rupee shares of two firms at Rs. 13 or at Rs. 16. If the first firm pays 5% dividend and the second firm says 6% dividend per annum, find:

(i) Which firm is paying better?

Ans: 1st firm:

N.V. of each share = Rs. 10 

M.V. of each share = Rs. 13

Dividend = 5% of Rs. 10

= Rs. $\left( {\dfrac{5}{{100}} \times 100} \right)$

= Rs. 0.50

Income percentage = $\dfrac{{income}}{{investment}} \times 100\% $  

= $\dfrac{{0.50}}{{13}} \times 100\% \; = 3.846\% $              

2nd firm:

N.V. of each share = Rs. 10

M.V. of each share = Rs. 16 

Dividend = 6% of Rs. 10

= Rs. $\left( {\dfrac{6}{{100}} \times 10} \right)$

= Rs. 0.60

Income percentage = $\dfrac{{income}}{{investment}} \times 100\% $  

= $\dfrac{{0.60}}{{16}} \times 100\% \; = 3.75\% $

Hence, the first firm is paying better than the second firm.

(ii) if Mr. Gupta  invests equally in both the firms and the difference between the returns from them is Rs. 30, find how much, in all, does he invest?

Ans: Let money invested in each firm be Rs. y

For 1st firm:

Number of shares purchased = $\dfrac{y}{{13\;}}shares$

Total dividend = Rs. $\left( {\dfrac{y}{{13}} \times 0.50} \right)$

= $\dfrac{y}{{26\;}}$

For 2nd firm:

Number of shares purchased = $\dfrac{y}{{16\;}}$ shares

Total dividend = Rs. $\left( {\dfrac{y}{{16}} \times 0.60} \right)$

= Rs. $\dfrac{{3y}}{{80\;}}$

Given: Difference of both dividend = Rs. 30

$\dfrac{y}{{26\;}}$ - $\dfrac{{3y}}{{80\;}}$ = Rs. 30

$\dfrac{y}{{1040\;}}$= Rs. 30

y = Rs. (30 x 1040) 

y = Rs. 31, 200

Total money invested in both firms = Rs. 31,200 $ \times $ 2 

= Rs. 62,400

10. Ashok invested Rs. 26,400 in 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475, find the:

(i) Number of shares he bought

Ans: Total dividend = Rs. 2,475

Dividend on each share = 12% of Rs. 25 

= Rs. $\left( {\dfrac{{12}}{{100}} \times 25} \right)$

= Rs. 3

Number of shares bought = $\dfrac{{Total\;dividend}}{{{\text{Dividend}}\,{\text{on}}\,1\,{\text{share}}}}$

= $\dfrac{{2475}}{3}$ 

= 825

(ii) Market value of each share.

Ans: Market value of 825 shares= Rs. 26,400

Market value of each share = $\dfrac{{Total\;investment}}{{No.\;of\;shares}}$

= $\dfrac{{26400}}{{825}}$ 

= Rs. 32

11. A man invested Rs. 45,000 in 15% Rs. 100 shares quoted at Rs. 125. When the M.V of these shares rose to Rs. 140, he sold some shares, just enough to raise Rs. 8,400. Calculate:

(i) The Number of Shares he Still Holds

Ans: Total investment = Rs. 45,000

Market value of 1 share = Rs. 125

Number of shares purchased = $\dfrac{{45000}}{{125}}$ 

= 360 shares

Nominal value of 360 shares = Rs. 100 $ \times $ 360 = Rs. 36000

Let number of shares sold = n 

Then sale price of 1 share = Rs. 140

Total sale price of n shares = Rs. 8,400

Then, n = $\dfrac{{8400}}{{140}}$ 

= 60 shares 

The number of shares he still holds = 360 - 60 = 300

(ii) The dividend due to him on these remaining shares.

Ans: Nominal value of 300 shares = Rs. 100 $ \times $ 300  

= Rs. 30,000

Dividend = 15% of Rs. 30,000

= Rs. $\left( {\dfrac{{15}}{{100}} \times 30000} \right)$

= Rs. 4,500

12. Mr. Tiwari invested Rs. 29,040 in 15% Rs. 100 shares quoted at a premium of 20%. Calculate:

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

Ans: Total investment = Rs. 29,040 

Nominal value of 1 share = Rs. 100

Market value of 1 share = Rs. 100 + 20% of Rs. 100

= Rs. 100 + Rs. $\left( {\dfrac{{20}}{{100}} \times 100} \right)$

= Rs. 100 + Rs. 20 

= Rs. 120

Number of shares purchased = $\dfrac{{29040}}{{120}}$ = 242 shares

(ii) Mr. Tiwari income from the investment.

Ans: Nominal value of 242 shares = Rs. 100 x 242 = Rs. 24,200

Dividend = 15% of Rs. 24,200

= Rs. $\left( {\dfrac{{15}}{{100}} \times 24,200} \right)$

= Rs. 3,630

(iii) The percentage return on his investment.

Ans: Income percentage = $\dfrac{{income}}{{investment}} \times 100\% $  

= $\dfrac{{3,630}}{{29,040}} \times 100\% \; = 12.5\% $

13. A dividend of 12% was declared on Rs. 150 shares selling at a certain price. If the rate of return is 10%, calculate:

(i) Market value of the shares

Ans: Nominal value of 1 share = Rs. 150

Dividend = 12% of Rs. 150 

= Rs. $\left( {\dfrac{{12}}{{100}} \times 150} \right)$

= Rs. 18

Let market value of 1 share = Rs. y 

Return = 10%

10% of Rs. y = Rs. 18 

$\dfrac{{10}}{{100\;}} \times y\; = \;18$ 

y = Rs. 180

(ii) The amount to be invested to obtain an annual dividend of Rs. 1350.

Ans: When dividend is Rs. 18, then investment = Rs. 180

When dividend is Rs. 1, then investment = Rs. $\dfrac{{180}}{{18\;}}$ 

= Rs. 10

When dividend is Rs. 1350, then investment

= $\;\dfrac{{180}}{{18\;}}x1350$

= Rs. 13,500  

14. Divide Rs. 50,760  into two parts such that if one art is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 100 shares at 8% premium , the annual incomes from both the investments are equal.

Ans: Total Investment = Rs. 50,760

Let 1st part be Rs. y

Then 2nd part = Rs. (50,760 – y) 

For 1st part:

N.V. of 1 share = Rs. 100

M.V. of 1 share = Rs. 100 - 8% of Rs. 100

= Rs. 100 - Rs. $\left( {\dfrac{8}{{100}} \times 100} \right)$ 

= Rs. 100 - Rs. 8 = Rs. 92

Number of shares purchased = $\dfrac{y}{{92}}$

Dividend on 1 share = 8% of Rs. 100

= Rs. $\left( {\dfrac{8}{{100}} \times 100} \right)$

= Rs. 8 

Total dividend = Rs. $\left( {\dfrac{y}{{92}} \times 8} \right)$

= Rs. $\dfrac{{2y}}{{23}}$

For 2nd part:

N.V. of 1 share = Rs. 100

M.V. of 1 share = Rs. 100 + 8% of Rs. 100

= Rs. 100 + Rs. $\left( {\dfrac{8}{{100}} \times 100} \right)$

= Rs. 100 + Rs. 8

= Rs. 108 

Number of shares purchased = $\dfrac{{50760\; - \;y}}{{108}}$  

Dividend on 1 share = 9% of Rs. 100 

= Rs. $\left( {\dfrac{9}{{100}} \times 100} \right)$

= Rs. 9

Total dividend = Rs. $\left( {\dfrac{{50760\; - \;y}}{{108}} \times 9} \right)$ 

= Rs. $\left( {\dfrac{{50760\; - \;y}}{{12}}} \right)$

Given that both dividend are equal:

$\dfrac{{2y}}{{23}}$ = $\dfrac{{50760\; - \;y}}{{12}}$

2y x 12 = 23 ($50760\; - \;y$)

24 y + 23 y = 23 x $50760$

y= $\dfrac{{23\; \times 50760}}{{47}}$

y = Rs. 24,840

1 part = Rs. 24,480                              

2 part = Rs. 50,760 - Rs. 24,480

= Rs. 25,920

15. Mr. Shameen invested 33$\dfrac{1}{3}\% $ of his savings in 2% Rs. 50 shares quoted at Rs. 60 and the remainder of the savings in 10% Rs. 100 shares quoted at Rs. 110. If his total income from these investments is Rs. 9,200, find;

(i) His Total Savings

Ans: Let his total savings be Rs. y

1st case:

His saving = 33$\dfrac{1}{3}\% \;of\;y$

= $\dfrac{y}{3}$

M.V. of 1 share = Rs. 60

Number of shares purchased = Rs. $\left( {\dfrac{y}{{3\; \times 60}} = \;\dfrac{y}{{180}}} \right)$ 

Dividend on 1 share = 20% of Rs. 50

= Rs. $\left( {\dfrac{{20}}{{100}} \times 50} \right)$

= Rs. 10

Total dividend = Rs. $\left( {\dfrac{y}{{180}} \times \;10} \right) = \;\dfrac{y}{{18}}\;$ 

2nd case:

His saving = 66 $\dfrac{2}{3}$ % of Rs. y

= Rs.$\dfrac{{2y}}{3}$ 

M.V. of 1 share = Rs. 110

Number of shares purchased = $\dfrac{{2y}}{{3\; \times \;110}} = \dfrac{y}{{165}}\;$ 

Dividend on 1 share = 10% of Rs. 100 

= Rs. $\left( {\dfrac{{10}}{{100}} \times 100} \right)$

= Rs. 10

Total dividend = Rs. $\left( {\dfrac{y}{{165}} \times 10} \right) = \;\dfrac{{2y}}{{33}}\;$ 

According to question:

Total income = Rs. 9,200

$\dfrac{y}{{18}}$ + $\dfrac{{2y}}{{23}}$ = Rs. 9,200 

$\dfrac{{23y}}{{198}}$= Rs. 9,200

y = $\dfrac{{9,200 \times 198}}{{23}}$

y = Rs. 79,200

Therefore, his total savings is Rs. 79,200.

(ii) The Number of Rs. 50 Shares

Ans: Number of Rs. 50 shares = $\dfrac{{79,200}}{{180}} = \;440$ 

(iii) The Number of Rs. 100 Shares

Ans: Number of Rs. 100 shares = $\dfrac{{79,200}}{{165}} = \;480$  

16. Vivek invests the number of Rs. 50 shares at Rs. 4,500 in 8%, Rs. 10 shares at Rs. 15. He sells the shares when the price rises to Rs. 30, and invests the proceeds in 12% Rs. 100 shares at Rs. 125. Calculate:

(i) The Sale Proceeds

Ans: Total investment = Rs. 4,500

M.V. of 1 share = Rs. 15

Number of shares purchased = $\dfrac{{4,500}}{{15}} = \;300$

N.V. of 1 share = Rs. 10 

N.V. of 300 shares = Rs. (10 $ \times $ 300) = Rs. 3,000

Dividend = 8% of Rs. 3,000 

= Rs. $\left( {\dfrac{8}{{100}} \times 3000} \right)$

= Rs. 240

Sale price of 1 share = Rs. 30

Total sale price = Rs. 30 $ \times $ 300 = Rs. 9000 

(ii) The Number of Rs. 125 Shares he Buys.

Ans: New market price of 1 share = Rs. 125 

So, number of shares purchased = $\dfrac{{9,000}}{{125}} = \;72$ shares 

(iii) The Change in his Annual Income from Dividend.

Ans: New nominal value of 1 share = Rs. 100

New nominal value of 72 shares = Rs. 100 $ \times $ 72 = Rs. 7, 200 

New dividend = 12% of Rs. 7,200

= Rs. $\left( {\dfrac{{12}}{{100}} \times 7200} \right)$

= Rs. 864

Change in annual income = Rs. 864 - Rs. 240

= Rs. 624

Therefore, change in annual income is Rs. 624.

16. Mr. Parekh invested Rs. 52,000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year he sells the shares at a premium of Rs. 20. Find:

(i) The Annual Dividend

Ans: Rate of dividend=8% 

Investment = Rs. 52,000

Market rate = Rs. 100 - Rs. 20

= Rs. 80  

Number of shares purchased = $\dfrac{{52000}}{{80}}$

= 650

Annual dividend = Rs. 650 $ \times $ 8 = Rs. 5200 

Therefore, annual dividend is Rs. 5,200.

(ii) The Profit Earned Including his Dividend.

Ans: Market price = Rs. 100 + Rs. 20

= Rs. 120

Sale price = Rs. 650 $ \times $ 120 = Rs. 78000

Profit = Rs. 78000 - Rs. 52000

= Rs. 26000

Total gain = Rs. 26000 + Rs. 5200 = Rs. 31200

Therefore, total gain is Rs. 31,200.

17. Salman buys 50 shares of face value Rs. 100 available at Rs. 132.

(i) What is his Investment?

Ans: Number of shares bought are 50

 N.V. of one share is Rs. 100.

 M.V. of each share is Rs. 132. 

Investment = M.V. of each share x Number of shares

= Rs. 132 $ \times $ 50 = Rs. 6600

Therefore, total investment is Rs. 6600.

(ii) If the Dividend is 7.5%, what will be his Annual Income?

Ans: Since dividend on 1 share:

= 7.5% of N.V.

= $\dfrac{{7.5}}{{100}} \times 100$    

= Rs. 7.50

So, Annual income = Rs. 7.50 $ \times $ 50 = Rs. 375

(iii) If he wants to increase his annual income by Rs. 150, how many extra shares should he buy? 

Ans: Extra shares to be bought =  $\dfrac{{Increase\;in\;annual\;income}}{{Income\;in\;one\;share}}$

= $\dfrac{{150}}{{7.50}} = \;20$ 

Therefore, extra shares to be bought are 20.

18. Salman invests a sum of money in Rs. 50 shares, saying 15% dividend quoted at 20% premium. If his annual dividend is Rs. 600, calculate:

(i) The Number of Shares he Bought.

Ans: N.V. of one share is Rs. 50.

M.V. of each share = Rs. 50 + 20% of Rs. 50

= Rs. 50 + \[\left( {\dfrac{{20}}{{100}} \times 50} \right)\]

= Rs. 50 + Rs. 10

= Rs. 60

Since dividend on 1 share:

= 15% of Rs. 50

= $\left( {\dfrac{{15}}{{100}} \times 50} \right)$

= Rs. 7.50

Numbers of share bought:

= $\dfrac{{Total\;dividend}}{{Dividend\;on\;one\;share}}$ = 80

(ii) His Total Investment.

Ans: Investment = M.V. of each share x Number of shares

= Rs. 60 $ \times $ 80 = Rs. 4800

Therefore, total investment is Rs. 4800.

(iii) The rate of return on his investment.

Ans: Rate of return = $\dfrac{{Totaldividend}}{{Total\;investment}} \times 100\% \;\;$

= $\dfrac{{600}}{{4800}} \times 100\% $

= 12.5% 

Therefore, the rate of return is 12.5%.

19. Rohit invested Rs. 9,600 on Rs. 100 shares at Rs. 20 premium paying 8% dividend. Rohit sold the shares when the price rose to Rs. 160. He invested the proceeds (excluding dividend) in 10% Rs. 50 shares at Rs. 40. Find the:

(i) Original Number of Shares.

Ans: N.V. of one share is Rs. 100.

M.V. of each share = Rs. 100 + Rs. 20 

= Rs. 120 

Money required to buy 1 share is Rs. 120.

Numbers of share bought:

= $\dfrac{{Money\;invested}}{{M.V.\;of\;one\;share\;\;}}$

= $\dfrac{{9600}}{{120}}$

= 80

(ii) Sale Proceeds,

Ans: Each share is sold at Rs. 160.

Sales proceeds = Rs. 80 $ \times $ 160 

= Rs. 12800

(iii) New Number of shares.

Ans: Investment = Rs. 12800.

Dividend = 10%

N.V. of 1 share = Rs. 50

M.V. of 1 share = Rs. 40

Numbers of shares bought = $\dfrac{{Money\;invested}}{{M.V.\;of\;1\;share}}$

= $\dfrac{{12800}}{{40}}$   

= 320

Thus, the number of shares is 320.

(iv) Change in the two dividends.

Ans: Dividend on 1 share = 10% of Rs. 50

= $\dfrac{{10}}{{100}} \times 50$

= Rs. 5

Dividend on 320 shares = Rs. 320 $ \times $ 5

= Rs. 1600

So, change in two dividends = Rs. 1600 - Rs. 640

= Rs. 960

20. How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.

Ans: N.V. of 1 share = Rs. 50

M.V. of 1 share = Rs. 60

Dividend = 10% of Rs. 50

= $\dfrac{{10}}{{100}} \times 50$

= Rs. 5

Numbers of share bought = $\dfrac{{Total\;dividend}}{{Dividend\;on\;one\;share\;\;}}$

= $\dfrac{{450}}{5}$

= 90

Investment = M.V. of each share x Number of shares

= Rs. 60 $ \times $ 90

= Rs. 5400

Rate of return = $\left( {\dfrac{{Total\;dividend}}{{Total\;Investment}} \times 100\% } \right)$

= $\dfrac{{450}}{{5400}} \times 100\% $

= 8.33%

$ \approx \;\,8\% $

Therefore, the rate of return is 8%.

Benefits of Vedantu Solutions of Chapter 3 - Shares and Dividend for Class 10 Mathematics ICSE:

With supportive arrangements by Vedantu, students don't have to lose the speed of attempting questions. Assume you are stuck on a question and for the appropriate solution, you want to skim through the pages of your course books to understand the thought and subsequently figure out the arrangement, which would break the stream. Notwithstanding the way that it causes obstruction, it is also monotonous. Moreover, when you have tests on your head, losing a bit of time can cause losing marks.

Handling Mathematics questions is one small step at a time interaction and staying over the issue is presumably going to happen. Likewise, as a curious student, you should know where you submitted the mistake. Going through a significant course perusing isn't only a period-taking cycle, nonetheless, you may not see exactly which place you made the blunder. With Vedantu it is amazingly direct. With Vedantu solutions of Class 10, you can see every subpart of the solution very minutely.

Vedantu emphasizes the situation of students when they are obstructed on account of a question and thus excessively explains each question with agreeable formulae and hypotheses so a student doesn't lose marks considering ICSE step marking. Selina Concise is seen as the base book for the ICSE board arranging and Vedantu helps students with attempting better.

Question Pattern

The ICSE Mathematics for Class X paper will be of more than 2 and a 1/2 hours term conveying a sum of 80 marks and an inward assessment of 20 marks. The test paper of Class 10 ICSE Mathematics will be isolated into two fragments, 1 and 2.

Segment I is a total of 40 marks,

Segment II is a total of 40 marks.

Segment I will have about short answer questions and in Section II, students need to go to any four out of seven questions.

A critical fragment of the test paper will have Shares and Dividend questions and students can practice better with Selina segment Shares and Dividend arrangements by Vedantu for Class X

Practicing various kinds of questions is an imperative strategy for getting ready for the test. Vedantu gives thought, keen learning and cognizance through game plan books. The plan of a question will expect data to be more than one part of the whole timetable. In addition, students ought to have this response for section 1 Shares and Dividend of Selina Concise accommodating. With Vedantu ruling in the Class X ICSE with a respectable rate opens ways to deal with new freedoms. Students find the opportunity to pick streams enthusiastically as demonstrated by their advantage.