Question

Amar invests Rs 25,000 in shares of per value Rs. 25 at 10% premium. The dividend is 20% per annum. Calculate the received by him annually.
(a) 4,545
(b) 5,545
(c) 5,454
(d) 6,545

Answer 1

Hint: To begin with, we will have the number of shares bought by Amar at Rs 25,000, if the cost of each share is Rs 25. Then we find the par value of the share if the premium is 10%. After finding the par value of each share, we will find the par value of the number of shares bought by Amar. The dividend of 20% will be calculated on this value.

Complete step by step answer:
It is given that Amar bought shares worth Rs 25000, when the price of each share is Rs 25.
So, the number of shares bought by Amar will be equal to the quotient of total money invested and price of each share.
$\Rightarrow \dfrac{25000}{25}=1000$
Therefore, Amar bought 1000 shares.
Let the par value of each share be x.
The value of each share is Rs 25 after adding the premium of 10%. Therefore (par value of each share + 10% of par value of each share = 25)
$\Rightarrow $ x + $\dfrac{10}{100}\text{x}$= 25
$\Rightarrow $ x + 0.1x = 25
$\Rightarrow $ 1.1x = 25
$\Rightarrow $ x = 22.72
Therefore, the par value of each share is Rs 22.72.
So, par value of 1000 shares will be (total number of shares $\times $ par value of each share)
$\Rightarrow $ 1000 $\times $ 22.72 = Rs 22,727
At the end of the year, Amar will receive a dividend of 20% on the par value of 1000 shares.
Therefore, 20% of par value of 1000 share is given by
$\Rightarrow \dfrac{20}{100}\times 22727$
$\begin{align}
  & \Rightarrow 0.2\times 22727 \\
 & \Rightarrow 4545.45 \\
\end{align}$
4545.45 is approximated as 4545.
Thus, at the end of the year, Amar will receive a dividend of Rs 4545.
Hence, option (a) is the correct option.

Note: It is not necessary for students to find the par value of each share. They can directly find the par value of 1000 shares at 10% from the investment of Rs 25,000.