The monthly incomes of two friends, Chetan and Vipul, are in the ratio 5:7, and each of them saves ₹96,000 per month. If the ratio of their monthly expenditures is 2:4, find Chetan’s monthly income (in ₹).

Let the monthly incomes of Chetan and Vipul be $ 5x \text{ and } 7x \text{ respectively.} $
Let their monthly expenditures be $ E_C \text{ and } E_V. $
We know: Savings = Income − Expenditure
$ 5x - E_C = 96,000 E_C = 5x - 96,000 $
$ 7x - E_V = 96,000 E_V = 7x - 96,000 $
Ratio of expenditures: $ \text E_C : E_V = 2 : 4 = 1 : 2 $
So, $ \frac{E_C}{E_V} = \frac{1}{2} $
$ \frac{5x - 96,000}{7x - 96,000} = \frac{1}{2} $
$ 2(5x - 96,000) = 1(7x - 96,000) $
$ 10x - 192,000 = 7x - 96,000 $
$ 10x - 7x = -96,000 + 192,000 $
$ 3x = 96,000 $
$ x = 32,000 $
Chetan’s monthly income = $ 5x = 5 \times 32,000 = 160,000 $
=160,000 ₹