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

Given :

A man spent 80% of his income and gave 10% of the remainder to the charity.

Money left with him $= Rs. 46260$

To do :

We have to find the income of the man.

Solution :

Let his income be Rs. P.

This implies,

Money spent $= Rs. \frac{80}{100} \times P = Rs. \frac{4}{5} P$

Money left after spending 80% of his income $= Rs. (P-  \frac{4}{5} P) = Rs. \frac{(5-4)}{5} P = Rs. \frac{1}{5} P$

Amount given to charity $= 10% of Rs. \frac{1}{5} P = \frac{10}{100} \times \frac{1}{5} P = Rs. \frac{1}{50} P$

Money left after giving charity $= Rs. (\frac{1}{5} P - \frac{1}{50} P) = Rs. \frac{(10-1)}{50} P = Rs. \frac{9}{50} P$

Therefore,

$46260 = \frac{9}{50} P$

$P = 46260 \times \frac{50}{9}$

$P = 5140 \times 50$

$P =Rs. 2,57,000$

The income of the person is Rs. 2,57,000.

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Updated on: 10-Oct-2022

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