Question

Amar invested Rs 25000 in shares of per value Rs 25 at a $10\%$ premium. The dividend is $20\%$ per annum. Calculate the rate of interest he gets on his money.
A). $12\%$
B). $12.12\%$
C). $18.18\%$
D). $13.12\%$

Answer 1

Hint: We will be using the concepts of profit and loss to solve the problem. Also, some concepts of percentage will be used to solve the problem easily. We will be using the formula - market value of a share = base value + $\%$ premium $\times $ base value.

Complete step-by-step solution
We have been given that Aman has invested money $=$ Rs 25,000
Now first we will have to find the number of shares that Aman has bought.
Let the share Aman has bought $=$ x
Now, we know that market value of a share $=$ base value \[+\%\] premium $\times $ base value
So, market value of one share
$=25+10\%25$
$\Rightarrow 25+\dfrac{10}{100}\times 25$
$\Rightarrow 25+2.5$
$\Rightarrow 27.5$
Now, we know that total money he invested in is Rs 25000
So,
$\Rightarrow 27.5x=25000$
$\Rightarrow x=\dfrac{25000}{27.5}$
$\therefore x=909$
Now we have the total share he purchased. To find the rate of interest he get on his money we have to find profit he gets as per dividend.
We know that dividend is always on base price therefore the total profit he received in a year
$\Rightarrow 20\%\left( 909\times 25 \right)$
$\Rightarrow \dfrac{20}{100}\times 22,725$
$\Rightarrow Rs4545$
Now, we can calculate interest he received as
$\Rightarrow \dfrac{profit}{money\ invested}\times 100$
$\Rightarrow \dfrac{4545}{25000}\times 100$
$\Rightarrow 18.18$
Hence, option (C) is correct.

Note: To solve this it is important to notice that the market value of a share \[=\ base\ value\ +\ base\ value\%\ premium\] also to find the total number of shares that can be purchased we have used the market price of the share. Also it is worthwhile to remember that \[\text{interest = }\dfrac{\text{profit}}{\text{money invested}}\ \times 100\]