The monthly incomes of two friends Sachin and Chetan, are in the ratio 5 : 7 respectively and each of them saves ₹96000 every month. If the ratio of their monthly expenditure is 2 : 3, find the monthly income of Sachin(in ₹).

Correct option is C

Given:

Sachin's monthly income : Chetan's monthly income = 5 : 7

Sachin's monthly expenditure : Chetan's monthly expenditure = 2 : 3

Savings of each = ₹96000

Formula used:

Income = Expenditure + Savings

Solution:

Let Sachin's income = 5x and Chetan's income = 7x
Let Sachin's expenditure = 2y and Chetan's expenditure = 3y

For Sachin:
Income = Expenditure + Savings
5x = 2y + 96000
y =$$\frac{(5x - 96000)}{2}$$​​

For Chetan:
Income = Expenditure + Savings
7x = 3y + 96000

Put y =$$\frac{(5x - 96000)}{2}$$​​

​$$7x = 3\left[\frac{(5x - 96000)}{2}\right] + 96000 \\ \ \\7x = \frac{(15x - 288000)}{2} + 96000 \\ \ \\7x = \frac{(15x - 288000 + 192000)}{2} \\ \ \\7x = \frac{(15x - 96000)}{2} \\ \ \\14x = 15x - 96000 \\ \ \\x = 96000$$​​

Sachin's monthly income = 5x = 5 × 96000 = ₹480000