Question

A man sells 60, Rs. 15 shares of a company paying 12 per cent dividend, at Rs. 21 each and invests the proceeds in Rs. 6 shares of another company at Rs. 9 each. Find his change in income, if the second company pays a dividend of 8 per cent.

Answer 1

Hint: In this type of question we have to use the concept of shares and dividend. We know that the initial value of a share written on the certificate is referred to as face value (FV) of the share while the price at which a share is exchanged or acquired by stock exchanges on the financial market is referred to as market value (MV). Also we will define dividend as the portion of a company’s taxable earnings paid to its owner, the dividend is based on share’s face value and independent of its market value.

Complete step by step answer:
Now, we have to find change income of a man if the second company pays a dividend of 8 per cent and we have provided that, the man sells 60, Rs. 15 shares of a company paying 12 per cent dividend, at Rs. 21 each and invests the proceeds in Rs. 6 shares of another company at Rs. 9 each.
We have given that the selling price of 1 share (Rs.15) is equal to Rs. 21
\[\begin{align}
  & \Rightarrow \text{Selling price of 60 }\left( \text{Rs}\text{.15} \right)\text{ shares }=21\times 60 \\
 & \Rightarrow \text{Selling price of 60 }\left( \text{Rs}\text{.15} \right)\text{ shares }=Rs.1260 \\
\end{align}\]
Also by given we can write
\[\begin{align}
  & \Rightarrow \text{Market price of Rs}\text{.6 share = Rs}\text{. 9} \\
 & \Rightarrow \text{Number of Rs}\text{.6 shares purchased = }\dfrac{1260}{9} \\
 & \Rightarrow \text{Number of Rs}\text{.6 shares purchased = 140} \\
\end{align}\]
Now as Rs. 15 shares of a company paying 12 per cent dividend we get,
\[\begin{align}
  & \Rightarrow \text{Dividend on 1 share of Rs}\text{. 15 = 12 }\!\!\%\!\!\text{ of Rs}\text{. 15} \\
 & \Rightarrow \text{Dividend on 1 share of Rs}\text{. 15 = }\dfrac{12}{100}\times 15 \\
 & \Rightarrow \text{Dividend on 1 share of Rs}\text{. 15 =}Rs.\left( \dfrac{9}{5} \right) \\
\end{align}\]
\[\begin{align}
  & \Rightarrow \text{Income on 60 }\left( \text{Rs}\text{. 15 shares} \right)=Rs.\left( \dfrac{9}{5} \right)\times 60 \\
 & \Rightarrow \text{Income on 60 }\left( \text{Rs}\text{. 15 shares} \right)=Rs.108 \\
\end{align}\]
Now, Rs. 6 shares of second company pays a dividend of 8 per cent
\[\begin{align}
  & \Rightarrow \text{Dividend on 1 share of Rs}\text{. 6 = 8 }\!\!\%\!\!\text{ of Rs}\text{. 6} \\
 & \Rightarrow \text{Dividend on 1 share of Rs}\text{. 15 = }\dfrac{8}{100}\times 6 \\
 & \Rightarrow \text{Dividend on 1 share of Rs}\text{. 15 =}Rs.0.48 \\
\end{align}\]
\[\begin{align}
  & \Rightarrow \text{Income on 140 }\left( \text{Rs}\text{. 6 shares} \right)=Rs.0.48\times 140 \\
 & \Rightarrow \text{Income on 140 }\left( \text{Rs}\text{. 6 shares} \right)=Rs.67.20 \\
\end{align}\]
Hence, we can find the change in the annual income as
\[\begin{align}
  & \Rightarrow \text{Change in the annual income }=Rs.108-Rs.67.20 \\
 & \Rightarrow \text{Change in the annual income }=Rs.40.80 \\
\end{align}\]
Hence, we can say that the annual income of the man decreased by \[Rs.40.80\].

Note: In this type of question students have to read the question carefully and then start to solve it. Students have to remember the definitions of face value, market value etc. Also students have to remember how to calculate the dividend on one share, income on number of shares etc.