A money lender finds that due to fall in the annual rate of interest from 8% to $${\text{7}}\frac{3}{4}{\text{%,}}$$  his yearly income diminishes by Rs. 61.50. His capital is = ?

Solution (By Examveda Team)

Let initial capital = 100 units

According to the question,
$$\eqalign{ & \frac{1}{4}{\text{unit = Rs}}{\text{. 61}}{\text{.50}} \cr & {\text{1 unit = Rs}}{\text{. 61}}{\text{.50}} \times {\text{4}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 246}} \cr & {\text{100 units = Rs}}{\text{. 24600}} \cr} $$
Hence,
Required capital = Rs. 24600

Alternate
Difference in percentage
$$\eqalign{ & {\text{ = 8% }} - \frac{{31}}{4}\% \cr & \Leftrightarrow \frac{1}{4}\% = 61.50 \cr & \Leftrightarrow 100\% = 24600 \cr} $$