Question

A man buys $ {\text{Rs 20}} $ shares paying $ 9\% $ dividend. The man wants to have an interest of = $ 12\% $ on his money. The market value of each share is:
A. $ {\text{Rs 12}} $
B. $ {\text{Rs 18}} $
C. $ {\text{Rs 15}} $
D. $ {\text{Rs 21}} $

Answer 1

Hint:
Here we need to know that the dividend is calculated on the nominal value and it is the earning of the person made on the investment or the market value of each share.
Here we can suppose the marked value as $ {\text{Rs }}x $
We can calculate the dividend on $ {\text{Rs 20}} $ which will be $ 9\% {\text{ of Rs 20}} $
Similarly we can calculate the profit of $ 12\% {\text{ on Rs }}x $ and equate both to get the value of the market price.

Complete step by step solution:
Here we are given that a man buys $ {\text{Rs 20}} $ shares paying $ 9\% $ dividend.
Let the market value of each share be $ {\text{Rs }}x $
So profit or the earning he made on the $ {\text{Rs 20}} $ shares $ = 9\% {\text{ of }}\;{\text{Rs 20}} = \dfrac{9}{{100}}(20) = {\text{Rs }}\dfrac{9}{5} $
This means that he earned $ {\text{Rs }}\dfrac{9}{5} $ on the investment of $ {\text{Rs }}x $
So he need to make the profit of $ 12\% $ on it
This will be equal to $ 12\% {\text{ of Rs }}x $
Profit of $ 12\% $ on $ x $ $ = $ $ 12\% {\text{ of Rs }}x $ $ = {\text{Rs}}\dfrac{{12x}}{{100}} $
Now we know that he wishes to make the interest of $ 12\% $ on his investment. Hence we can say that
Profit of $ 12\% $ on $ {\text{Rs }}x $ $ = $ $ {\text{Rs }}\dfrac{9}{5} $
Hence we can substitute their values over here and get the desired unknown $ x $ which is the market value of the share.
 $ {\text{Rs}}\dfrac{{12x}}{{100}} $ $ = {\text{Rs }}\dfrac{9}{5} $
 $ \dfrac{{12x}}{{100}} $ $ = \dfrac{9}{5} $
So we get the simpler equation, now we can easily solve for the value of the unknown $ x $
 $ x = \dfrac{{9(100)}}{{12(5)}} = \dfrac{{900}}{{60}} = 15 $
So we get that the man bought each share from the market at the price of $ {\text{Rs 15}} $

Hence we can say that C is the correct option.

Note:
Here we must keep in mind that the dividend is calculated on the nominal value. We must not make the mistake of calculating the $ 9\% $ dividend on $ {\text{Rs }}x $
We must know the concept of the dividend and how the shares are invested for the profit of the person.