Question

Raman Spends 2/5 of his monthly income on food and 3/8 of the remaining on clothes. Find the following:-
a. What fraction of his income is left with him?
b. If the money left is ₹2400, find his monthly income.

Answer 1

Given:

$\text{Fraction of his income spent on food } = \dfrac{2}{5}$

Find the fraction of his money left:

$\text{Fraction of his income left } = 1 - \dfrac{2}{5}$

$\text{Fraction of his income left } = \dfrac{5}{5} - \dfrac{2}{5}$

$\text{Fraction of his income left } = \dfrac{3}{5}$

Find the fraction of his money spent on clothes:

$\text{Fraction of his income spent on clothes } = \dfrac{3}{8} \text{ of his remaining money}$

$\text{Fraction of his income spent on clothes } = \dfrac{3}{8} \times \dfrac{3}{5}$

$\text{Fraction of his income spent on clothes } = \dfrac{9}{40}$

Find the fraction of his income left:

$\text{Fraction of his income left } = \dfrac{3}{5} - \dfrac{9}{40}$

$\text{Fraction of his income left } = \dfrac{24}{40} - \dfrac{9}{40}$

$\text{Fraction of his income left } = \dfrac{15}{40}$

$\text{Fraction of his income left } = \dfrac{3}{8}$

Find his income:

$\text{Fraction of his income left } = \dfrac{3}{8}$

$\text{Fraction of his income left } = 2400$

$\dfrac{3}{8} \text { of his income} = 2400$

$\dfrac{1}{8} \text { of his income} = 2400 \div 3$

$\dfrac{1}{8} \text { of his income} = 800$

$\text{ His income} = 800 \times 8$

$\text{ His income} = 6400$

Answer: (a) 3/8 of his income is left. (b) His income is ₹6400