The monthly incomes of two friends Nirmal and Rakesh, are in the ratio 5 : 7 respectively and each of them saves ₹84000 every month. If the ratio of their monthly expenditure is 2 : 4, find the monthly income of Nirmal(in ₹).

Correct option is C

Given:

The monthly incomes of Nirmal and Rakesh are in the ratio 5 : 7.

Monthly savings of Nirmal and Rakesh = ₹84000 each.

The ratio of their monthly expenditures = 2 : 4.

Formula used:
Income = Savings + Expenditure

Solution:
Let the monthly incomes of Nirmal and Rakesh be ₹5x and ₹7x respectively.

Let the monthly expenditures of Nirmal and Rakesh be ₹2y and ₹4y respectively.

Income = Savings + Expenditure

For Nirmal:
5x = 84000 + 2y
2y = 5x - 84000

For Rakesh:
7x = 84000 + 4y
4y = 7x - 84000

Divide both equations to eliminate y:

​$$\frac{2y}{4y} = \frac{5x - 84000}{7x - 84000} \\ \ \\ \frac{1}{2} = \frac{5x - 84000}{7x - 84000} \\ \ \\ 7x - 84000 = 2(5x - 84000) \\ \ \\ 7x - 84000 = 10x - 168000 \\ \ \\ 168000 - 84000 = 10x - 7x \\ 84000 = 3x \\ x = 28000$$​​

Monthly income of Nirmal = 5x = 5 × 28000 = 140000