Question

After spending 80% of his income and giving 10% of the remainder in a charity, a man has Rs 46260 left with him. Find his income.

Answer 1

Let the income of the man be Rs x.
Then, income spent = 80% of Rs. x
= Rs $\left(\frac{80}{100}\times x\right)$ = Rs $\left(\frac{80x}{100}\right)$ = Rs $\left(\frac{4x}{5}\right)$
Amount left after all the expenditure = Rs $\left(x-\frac{4x}{5}\right)$ = Rs $\left(\frac{5x-4x}{5}\right)$ = Rs $\left(\frac{x}{5}\right)$
Amount given to the charity = 10% of Rs $\left(\frac{x}{5}\right)$
= Rs $\left(\frac{10}{100}\times \frac{x}{5}\right)$ = Rs $\left(\frac{10x}{500}\right)$= Rs $\left(\frac{x}{50}\right)$
Amount left after the charity = Rs $\left(\frac{x}{5}-\frac{x}{50}\right)$
= Rs $\left(\frac{10x-x}{50}\right)$ = Rs $\left(\frac{9x}{50}\right)$
Now, we have:
Rs $\left(\frac{9x}{50}\right)$ = Rs 46260
∴ x = Rs $\left(\frac{46260\times 50}{9}\right)$ = Rs 257000
Hence, the income of the man is Rs 2,57,000.