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 3000 per month, find the monthly income of each.

Answer 1

Let the monthly income and expenditure of A be Rs. 5x and Rs. 7y, respectively.
Let the monthly income and expenditure of B be Rs. 4x and Rs. 5y,​ respectively.
Then, we have:
5x − 7y = 3000 ...(i)
4x − 5y = 3000 ...(ii)
On multiplying (i) by 5 and (ii) by 7, we get:
25x − 35y = 15000 ...(iii)
28x − 35y = 21000 ...(iv)
On subtracting (iii) from (iv), we get:
3x = 6000
⇒ x = 2000
On substituting x = 2000 in (i), we get:
5 × 2000 − 7y = 3000
⇒ −7y = 3000 − 10000 = −7000
⇒ y = 1000
∴ Income of A = 5x = 5 × 2000 = Rs. 10000
∴ Income of B = 4x = 4 × 2000 = Rs. 8000