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 $= 100 \ Rs.$

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

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

Therefore

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

$9(100+x) = 675$

$\Rightarrow x = -25$

Therefore the market price of the share $= 100-25 = 75 \ Rs.$

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

Answer:

Nominal Price of the share $= 25 \ Rs.$

Market Price of the share $= 40 \ Rs.$

Number of Shares bought $= 60$

Let the % dividend $= x \ %$

Therefore

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

$\Rightarrow 25x = 160 \ or \ x = 6.4\%$

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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 $= 100 \ Rs.$

Market Price of the share $= 120 \ Rs.$

Let the % dividend $= x \ %$

Let us say that the person bought 100 shares.

Therefore

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

$\Rightarrow 100x = 120 \times 15 \ or \ x = 18\%$

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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 $= x \ Rs.$

Therefore Market Price of the share $= 0.9x \ Rs.$

Number of Shares bought $= 50$

Let the % dividend $= y \ %$

Therefore

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

$\Rightarrow y = 0.9 \times 20 \ or \ y = 18\%$

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Question 5: A company declares 8 per cent 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 $= x \ Rs.$

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

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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 $= 100 \ Rs.$

Market Price of the share $= 110 \ Rs.$

Let the number of Shares bought $= x$

Therefore

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

Hence the investment $= 140 \times 110 = 15400 \ Rs.$

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Question 7: A company declares a dividend of 11.2% to all its share holders. If its 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 $= 60 \ Rs.$

Market Price of the share $= 75 \ Rs.$

Let the number of Shares bought $= x$

Therefore

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

Hence the investment $= 250 \times 75 = 18750 \ Rs.$

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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 $= 20 \ Rs.$

Market Price of the share $= 24 \ Rs.$

The number of Shares bought $= 400$

Amount invested $= 400 \times 24 = 9600 \ Rs.$

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

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

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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 $= 20 \ Rs.$

Market Price of the share $= 16 \ Rs.$

The number of Shares bought $= 400$

Amount invested $= 400 \times 16 = 6400 \ Rs.$

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

Let the rate of dividend $= x\%$

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

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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:

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

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

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

Therefore the investment $= 72x$

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

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Question 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.

Answer:

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

Investment $= 1800 \times 140 = 252000 \ Rs.$

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

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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:

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

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

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

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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 $= 60 \times 100 = 6000 \ Rs.$

Sale Proceeds $= 60 \times 160 = 9600 \ Rs.$

New Investment is at Rs. 48 per share

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

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

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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 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:

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

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

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

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

Answer:

First Investment

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

Investment $= 100 \times 80 = 8000 Rs.$

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

Second Investment

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

Investment $= 100 \times 120 = 12000 Rs.$

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

Hence the first investment is better.

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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

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

Investment $= 100 \times 120 = 12000 \ Rs.$

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

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

Second Company

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

Investment $= 100 \times 132 = 13200 \ Rs.$

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

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

Therefore the Second company gives a better return.

Difference between the annual return = 200 Rs.

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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 shares 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

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

Second Investment

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

Hence difference in income $= 1177.2 - 432 = 745.2 \ Rs.$

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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:

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

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

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

Hence the difference $= 200 \ Rs.$

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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 equal dividend at the end of the year, find the rate percent of the dividend received by B.

Answer:

Brother A

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

Brother B

Dividend = 600 Rs.

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

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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:

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

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

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

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Question 21: A person invested Rs. 19,200 in 15% Rs. 100 shares at 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 $= 100 \ Rs.$

Market Price of the share $= 80 \ Rs.$

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

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

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

Second Investment

Nominal Price of the share $= 50 \ Rs.$

Market Price of the share $= 42 \ Rs.$

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

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

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

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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 $= 100 \ Rs.$

Market Price of the share $= 120 \ Rs.$

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