Question

A dividend of 9 % was declared on Rs.100 shares selling at a certain price.
If the return rate is 7.5 % , find the investment required to earn Rs.630.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{market}\mathrm{value}\mathrm{of}1\mathrm{share}=\mathrm{Rs}\mathrm{x} \\ \mathrm{Now},\mathrm{face}\mathrm{value}\mathrm{of}1\mathrm{share}=\mathrm{Rs}100 \\ \mathrm{Dividend}\mathrm{on}1\mathrm{share}=9\%\mathrm{of}\mathrm{Rs}100=\frac{9}{100}\times 100=\mathrm{Rs}9 \\ \mathrm{Profit}\mathrm{on}1\mathrm{share}=7\frac{1}{2}\%\mathrm{of}\mathrm{Rs}\mathrm{x}=\frac{15}{200}\times \mathrm{x}=\mathrm{Rs}\left[\frac{15\mathrm{x}}{200}\right] \\ \mathrm{Now},\frac{15\mathrm{x}}{200}=9 \\ \Rightarrow \mathrm{x}=\frac{9\times 200}{15}=120 \\ \mathrm{So},\mathrm{Market}\mathrm{value}\mathrm{of}1\mathrm{share}=\mathrm{Rs}120 \\ \mathrm{Now},\mathrm{investment}=\mathrm{Market}\mathrm{value}\mathrm{of}1\mathrm{share}\times \mathrm{Number}\mathrm{of}\mathrm{shares} \\ \Rightarrow \mathrm{investment}=120\times \frac{\mathrm{Annual}\mathrm{income}}{\mathrm{income}\mathrm{on}1\mathrm{share}} \\ \Rightarrow \mathrm{investment}=120\times \frac{630}{9} \\ \Rightarrow \mathrm{investment}=\mathrm{Rs}8400 \end{gathered}$$