Question

The monthly incomes of A and B are in the ratio of 5:4 and their monthly expenditures are in the ratio of 7:5. If each saves Rs. 9000 per month, find the monthly income of each.

Answer 1

Let the monthly income of A and B are Rs.x and Rs.y respectively.

Then as per the question

`x/y = 5/4`

⇒ `y = (4x)/5`

Since each save Rs.9,000, so

Expenditure of A = Rs.(x – 9000)

Expenditure of B = Rs.(y – 9000)

The ratio of expenditures of A and B are in the ratio 7:5.

`∴(x−9000)/(y−9000) = 7/5`

⇒ 7y – 63000 = 5x – 45000

⇒ 7y – 5x = 18000

From (i), substitute y = `(4x)/5` in (ii) to get

`7 × (4x)/5  –  5x = 18000`

⇒ 28x – 25x = 90000

⇒ 3x = 90000

⇒ x = 30000

Now, putting x = 30000, we get

`y = (4 ×30000)/5 = 4 × 6000 = 24000`

Hence, the monthly incomes of A and B are Rs. 30,000 and Rs.24,000.