Class 10: Shares and Dividend – Exercise 5(b) – ICSE / ISC / CBSE Mathematics Portal for K12 Students

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

Answer:

Nominal Price of the share $\displaystyle = 100 \text{ Rs. }$

Let the Market Price of the share $\displaystyle = (100+x) \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 75 \times 100 \times \frac{9}{100} = 675 \text{ Rs. }$

Therefore

$\displaystyle \frac{12}{100} \times 75 \times (100+x) = 675$

$\displaystyle 9(100+x) = 675$

$\displaystyle \Rightarrow x = -25$

Therefore the market price of the share $\displaystyle = 100-25 = 75 \text{ Rs. }$

$\displaystyle \\$

Question 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?

Answer:

Nominal Price of the share $\displaystyle = 25 \text{ Rs. }$

Market Price of the share $\displaystyle = 40 \text{ Rs. }$

Number of Shares bought $\displaystyle = 60$

Let the % dividend $\displaystyle = x %$

Therefore

$\displaystyle 60 \times 25 \times \frac{x}{100} = 60 \times 40 \times \frac{4}{100}$

$\displaystyle \Rightarrow 25x = 160 \text{ or } x = 6.4\%$

$\displaystyle \\$

Question 3: 100 Rs. 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%.

Answer:

Nominal Price of the share $\displaystyle = 100 \text{ Rs. }$

Market Price of the share $\displaystyle = 120 \text{ Rs. }$

Let the % dividend $\displaystyle = x %$

Let us say that the person bought 100 shares.

Therefore

$\displaystyle 100 \times 100 \times \frac{x}{100} = 100 \times 120 \times \frac{15}{100}$

$\displaystyle \Rightarrow 100x = 120 \times 15 \text{ or } x = 18\%$

$\displaystyle \\$

Question 4: 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%.

Answer:

Let Nominal Price of the share $\displaystyle = x \text{ Rs. }$

Therefore Market Price of the share $\displaystyle = 0.9x \text{ Rs. }$

Number of Shares bought $\displaystyle = 50$

Let the % dividend $\displaystyle = y %$

Therefore

$\displaystyle 50 \times x \times \frac{y}{100} = 50 \times 0.9x \times \frac{20}{100}$

$\displaystyle \Rightarrow y = 0.9 \times 20 \text{ or } y = 18\%$

$\displaystyle \\$

Question 5: A company declares an 8 percent dividend to the shareholders. If a man receives Rs. 2840 as his dividend, find the nominal value of his shares.

Answer:

Let the nominal Value of the shares $\displaystyle = x \text{ Rs. }$

$\displaystyle \text{Therefore } x \times \frac{8}{100} = 2840 \Rightarrow x = 35500 \text{ Rs. }$

$\displaystyle \\$

Question 6: How much should a man invest in Rs. 100 shares selling at Rs. 110 to obtain an annual income of Rs. 1680, if the dividend declared is 12%?

Answer:

Nominal Price of the share $\displaystyle = 100 \text{ Rs. }$

Market Price of the share $\displaystyle = 110 \text{ Rs. }$

Let the number of Shares bought $\displaystyle = x$

Therefore

$\displaystyle x \times 100 \times \frac{12}{100} = 1680 \Rightarrow x = 140$

Hence the investment $\displaystyle = 140 \times 110 = 15400 \text{ Rs. }$

$\displaystyle \\$

Question 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 a person invest, in buying the shares of this company, in order to have an annual income of Rs. 1680?

Answer:

Nominal Price of the share $\displaystyle = 60 \text{ Rs. }$

Market Price of the share $\displaystyle = 75 \text{ Rs. }$

Let the number of Shares bought $\displaystyle = x$

Therefore

$\displaystyle x \times 60 \times \frac{11.2}{100} = 1680 \Rightarrow x = 250$

Hence the investment $\displaystyle = 250 \times 75 = 18750 \text{ Rs. }$

$\displaystyle \\$

Question 8: A man buys 400, 20 Rs. shares at a premium of Rs. 4 each and receives a dividend of 12%. Find i) The amount invested by him; ii) His total income from the shares. iii) Percentage return on his money;

Answer:

Nominal Price of the share $\displaystyle = 20 \text{ Rs. }$

Market Price of the share $\displaystyle = 24 \text{ Rs. }$

The number of Shares bought $\displaystyle = 400$

Amount invested $\displaystyle = 400 \times 24 = 9600 \text{ Rs. }$

$\displaystyle \text{Income from the shares } = 400 \times 20 \times \frac{12}{100} = 960 \text{ Rs. }$

$\displaystyle \% \text{ return on his money } = \frac{960}{9600} \times 100 = 10\%$

$\displaystyle \\$

Question 9: A man buys 400, 20 Rs. shares at a discount of 20% and receives a return of 12% on his money. Calculate: i) The amount invested by him; ii) The rate of dividend paid by the company.

Answer:

Nominal Price of the share $\displaystyle = 20 \text{ Rs. }$

Market Price of the share $\displaystyle = 16 \text{ Rs. }$

The number of Shares bought $\displaystyle = 400$

Amount invested $\displaystyle = 400 \times 16 = 6400 \text{ Rs. }$

$\displaystyle \text{ Return on investment } = \frac{12}{100} \times 6400 = 768 \text{ Rs. }$

Let the rate of dividend $\displaystyle = x\%$

$\displaystyle \text{Therefore } 400 \times 20 \times \frac{x}{100} = 768 \Rightarrow x = 9.6\%$

$\displaystyle \\$

Question 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? ii) What should 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 paid for each share.

Answer:

$\displaystyle \text{Annual Dividend } = 10000 \times 100 \times \frac{5}{100} = 50000 \text{ Rs. }$

$\displaystyle \text{Annual income of the man } = 72 \times 100 \times \frac{5}{100} = 360 \text{ Rs. }$

Let the price of the share he bought was $\displaystyle x$

Therefore the investment $\displaystyle = 72x$

Hence $\displaystyle 72x \times \frac{4}{100} = 360 \Rightarrow x = 125 \text{ Rs. }$

$\displaystyle \\$

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

Answer:

Annual dividend $\displaystyle \text{ } = 1800 \times 100 \times \frac{15}{100} = 27000 \text{ Rs. }$

Investment $\displaystyle = 1800 \times 140 = 252000 \text{ Rs. }$

% return $\displaystyle = \frac{27000}{252000} \times 100 = 10.71\%$

$\displaystyle \\$

Question 12: man invests Rs. 11200 in a company paying 6% per annum when its Rs. 100 shares can be bought for Rs. 140. Find; i) His annual dividend ii) His % return on his investment

Answer:

$\displaystyle \text{Number of shares bought } = \frac{11200}{140} = 80$

$\displaystyle \text{Annual dividend } = 80 \times 100 \times \frac{6}{100} = 480$

$\displaystyle \text{Percentage return } = \frac{480}{11200} \times 100 = 4.29\%$

$\displaystyle \\$

Question 13: A person has 60 shares of Nominal Value 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 paying 18% dividend annually. Calculate; i) The sale proceeds; ii) The number of shares he buys and iii) His annual dividend from the shares.

Answer:

Initial Investment $\displaystyle = 60 \times 100 = 6000 \text{ Rs. }$

Sale Proceeds $\displaystyle = 60 \times 160 = 9600 \text{ Rs. }$

New Investment is at Rs. 48 per share

Number of shares bought $\displaystyle = \frac{9600}{48} = 200$

$\displaystyle \text{Annual dividend } = 200 \times 50 \times \frac{18}{100} = 1800 \text{ Rs. }$

$\displaystyle \\$

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

Answer:

$\displaystyle \text{Total dividend paid } = 10000 \times 100 \times \frac{8}{100} = 80000 \text{ Rs. }$

$\displaystyle \text{The dividend man will receive } = 90 \times 100 \times \frac{8}{100} = 720 \text{ Rs. }$

$\displaystyle \% \text{ return on his investment } = \frac{720}{90 \times 150} \times 100 = 5.33\%$

$\displaystyle \\$

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

Answer:

First Investment

$\displaystyle \text{Dividend on }16\% \text{ Rs. 100 shares at 80 }= 100 \times 100 \times \frac{16}{100} = 1600 \text{ Rs. }$

Investment $\displaystyle = 100 \times 80 = 8000 \text{ Rs. }$

$\displaystyle \text{return } = \frac{1600}{8000} \times 1000 = 20\%$

Second Investment

$\displaystyle \text{Dividend on } 20\% \text{ Rs. 100 shares at 100 }= 100 \times 100 \times \frac{20}{100} = 2000 \text{ Rs. }$

Investment $\displaystyle = 100 \times 120 = 12000 \text{ Rs. }$

$\displaystyle \% \text{return } = \frac{2000}{12000} \times 1000 = 16.67\%$

Hence the first investment is better.

$\displaystyle \\$

Question 16: A man has a choice to invest in 200 Rs. shares of two firms at Rs. 120 or at 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. 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.

Answer:

First Company

$\displaystyle \text{Dividend earned } = 100 \times 200 \times \frac{5}{100} = 1000 \text{ Rs. }$

Investment $\displaystyle = 100 \times 120 = 12000 \text{ Rs. }$

% return $\displaystyle = \frac{1000}{12000} \times 100 = 8.33\%$

$\displaystyle \text{Return on investment of Rs. 26400 } = \frac{26400}{120} \times 200 \times \frac{5}{100} = 2200 \text{ Rs. }$

Second Company

$\displaystyle \text{Dividend earned } = 100 \times 200 \times \frac{6}{100} = 1200 \text{ Rs. }$

Investment $\displaystyle = 100 \times 132 = 13200 \text{ Rs. }$

% return $\displaystyle = \frac{1200}{13200} \times 100 = 9.09\%$

$\displaystyle \text{Return on investment of Rs. 26400} = \frac{26400}{132} \times 200 \times \frac{6}{100} = 2400 \text{ Rs. }$

Therefore the Second company gives a better return.

Difference between the annual return = 200 Rs.

$\displaystyle \\$

Question 17: A man bought 360, 10 Rs. shares of a company, paying 12% per annum. He sold the shares when their price rose to Rs. 21 per share and invested the proceeds in 5 rupees shares paying 4.5% per annum at Rs. 3.50 per share. Find the annual change in his income.

Answer:

First Investment

$\displaystyle \text{Dividend income } = 360 \times 10 \times \frac{12}{100} = 432 \text{ Rs. }$

Second Investment

$\displaystyle \text{Dividend income } = \frac{360 \times 21}{3.50} \times 5 \times \frac{4.5}{100} = 1177.2 \text{ Rs. }$

Hence difference in income $\displaystyle = 1177.2 - 432 = 745.2 \text{ Rs. }$

$\displaystyle \\$

Question 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 he buy and What was the change in his income?

Answer:

$\displaystyle \text{Income from first investment } = 400 \times 20 \times \frac{5}{100} = 4000 \text{ Rs. }$

$\displaystyle \text{No of Rs. 10 shares bought } = \frac{400 \times 18}{12} = 600$

$\displaystyle \text{Dividend income } = 600 \times 10 \times \frac{7}{100} = 4200 \text{ Rs. }$

Hence the difference $\displaystyle = 200 \text{ Rs. }$

$\displaystyle \\$

Question 19: Two brothers A and B invests Rs. 16,000 each in buying shares of two companies. A buys 3% 100 Rs. shares at 80 and B buys 10 Rs. shares at par. If they both receive an equal dividend at the end of the year, find the rate percent of the dividend received by B.

Answer:

Brother A

$\displaystyle \text{Dividend } = \frac{16000}{80} \times 100 \times \frac{3}{100} = 600 \text{ Rs. }$

Brother B

Dividend = 600 Rs.

$\displaystyle \frac{16000}{10} \times 10 \times \frac{x}{100} = 600 \Rightarrow x = 3.75\%$

$\displaystyle \\$

Question 20: A man invests Rs. 20,020 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; ii) The dividend he receives annually; iii) The rate of interest he gets on his money. [2012]

Answer:

$\displaystyle \text{Number of shares } = \frac{20020}{26+2.6} = 700$

$\displaystyle \text{Dividend } = 700 \times 26 \times \frac{15}{100} = 2730 \text{ Rs. }$

$\displaystyle \% \text{ rate of interest he gets } = \frac{2730}{20020} \times 100 = 13.64\%$

$\displaystyle \\$

Question 21: A person invested Rs. 19,200 in 15% Rs. 100 shares at a 20% discount. After a year She sold these shares at Rs. 90 each and invested the proceeds (including her dividend) in 20%, Rs. 50 shares at Rs. 42. Find: i) The number of shares he buys. ii) The dividend he receives annually; iii) The rate of interest he gets on his money.

Answer:

First Investment

Nominal Price of the share $\displaystyle = 100 \text{ Rs. }$

Market Price of the share $\displaystyle = 80 \text{ Rs. }$

$\displaystyle \text{Number of shares } = \frac{19200}{80} = 240$

$\displaystyle \text{Dividend Income } = 240 \times 100 \times \frac{15}{100} = 3600 \text{ Rs. }$

$\displaystyle \text{Rate of interest } = \frac{3600}{19200} \times 100 = 18.75\%$

Second Investment

Nominal Price of the share $\displaystyle = 50 \text{ Rs. }$

Market Price of the share $\displaystyle = 42 \text{ Rs. }$

$\displaystyle \text{Number of shares } = \frac{240 \times 90 + 3600}{42} = 600$

$\displaystyle \text{Dividend Income } = 600 \times 50 \times \frac{20}{100} = 6000 \text{ Rs. }$

$\displaystyle \text{Rate of interest } = \frac{6000}{25200} \times 100 = 23.08\%$

$\displaystyle \\$

Question 22: A person invested Rs. 19,200 in 15% Rs. 100 shares at 20% premium. After a year She sold these shares at Rs. 140 each and invested the proceeds (including her dividend) in 20%, Rs. 20 shares at Rs. 16. Find i) dividend for the first year ii) annual income in the second year, iii) % change in the return on her original investment.

Answer:

First Investment

Nominal Price of the share $\displaystyle = 100 \text{ Rs. }$

Market Price of the share $\displaystyle = 120 \text{ Rs. }$

$\displaystyle \text{Number of shares } = \frac{19200}{120} = 160$