Question

The monthly incomes of two friends Amit and Gopal, are in the ratio 5 : 7 respectively and each of them saves ₹72000 every month. If the ratio of their monthly expenditure is 2 : 3, find the monthly income of Amit(in ₹).

• A. 360000
• B. 359000
• C. 504000
• D. 361000

Answer 1

Answer:

A. 360000

The monthly income of Amit is ₹3,60,000.

1. Set up the equations for income

The ratio of the monthly incomes of Amit and Gopal is 5 : 7.

Let Amit's income = 5x

Let Gopal's income = 7x

2. Relate income, savings, and expenditure

We know that: Expenditure = Income − Savings

Each friend saves ₹72,000 per month.

• Amit's expenditure = 5x - 72000

• Gopal's expenditure = 7x - 72000

3. Use the expenditure ratio to solve for x

The ratio of their monthly expenditures is 2 : 3.

$\frac{5x-72000}{7x-72000}=\frac{2}{3}$

Cross-multiply to solve the equation:

3(5x-72000)=2(7x-72000)

15x-216000=14x-144000

15x-14x=216000-144000

x=72000

4. Calculate Amit's income

Amit's income = $5x = 5 \times 72000 = \mathbf{3,60,000}$