# Problems on Shares and Dividends

We will discuss here some of the problems on shares and dividends.

1. Michael buys shares of face value $50 of a company which pays 10 % dividend. At what price did he buy each share from the market if his profit is 16 % on his investment? Solution: Let the market value (M.V.) of each share be x. The dividend is calculated on nominal value. The dividend on one share = 10% of$ 50 = $5. Therefore, he earned$ 5 on an investment of x.

A profit of 16 % on x = $$\frac{16}{100}$$ × x = $$\frac{4x}{25}$$

Therefore, $$\frac{4x}{25}$$ = $5 ⟹ x =$$$\frac{25 × 5}{4}$$

⟹ x = $$$\frac{125}{4}$$ ⟹ x =$ 31.25

Therefore, Michael bought each share at $31.25 from the market. 2. Jackson buys a$ 40 shares in a company, which pays 10% dividend. Jackson buys the share at such a price that his profit is 16% on his investment. At what price did Jackson buy the share?

Solution:

Dividend (profit) given by the company on 1 share = 10% of $40 =$ 4.

Suppose the man buys one share for x.

Therefore, Jackson’s profit = 16% of $x =$ $$\frac{16x}{100}$$

According to the problem, $$\frac{16x}{100}$$ = 4

⟹ x = $25 Jackson bought the share at$ 25.

3. Robert bought shares of 6% $100 shares at$ 120. Adrian bought shares of 8% $20 shares at$ 30. Whose investment was better?

Solution:

6% $100 shares at$ 120

i.e., the annual income from 1 share of nominal value $100 is$ 6, investment for 1 share being $120. Therefore, profit percentage = $$\frac{6}{120}$$ × 100 % = 5% Therefore, Robert’s shares give him a profit of 5% 8 %$ 20 shares at $30 i.e., the annual income from 1 share of nominal value$ 20 is $$$\frac{8 × 20}{100}$$ =$ $$\frac{8}{5}$$, investment for 1 share being \$ 30.

Profit percentage = $$\frac{\frac{8}{5}}{ 30}$$ × 100 %

= $$\frac{16}{3}$$ %

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

Therefore, Adrian’s shares give him a profit of 5$$\frac{1}{3}$$%

Shares and Dividends

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