The incomes of A and B are in the ratio 3 : 2 and their expenditures are in the ratio 5 : 3. If each saves ₹2,000, what will be the difference between their incomes?

Correct option is A

Given:

The income ratio of A and B is 3 : 2.

The expenditure ratio of A and B is 5 : 3.

Both A and B save ₹2,000.

Formula Used:

Savings = Income – Expenditure

Solution:

Let the incomes of A and B be 3x and 2x respectively. Let the expenditures of A and B be 5y and 3y respectively.

The savings for both A and B are ₹2,000 each:

Savings of A = 3x − 5y = 2000

Savings of B = 2x − 3y = 2000

Subtract equation (2) from equation (1):

(3x - 5y) - (2x - 3y) = 2000 - 2000

3x - 5y - 2x + 3y = 0

x - 2y = 0

x = 2y

Substitute x = 2y into the second equation:

2(2y) - 3y = 2000

4y - 3y = 2000

y = 2000

Now that we know y = 2000, substitute this into x = 2y:

x=2 × 2000 = 4000

Income of A = 3x = 3 × 4000 = 12,000  and Income of B = 2x = 2 × 4000 = 8,000

The difference between their incomes = 12,000 - 8,000 = 4,000

The difference between their incomes is ₹4,000.