Question

The monthly incomes of two persons are in the ratio 9 : 7 and their monthly expenditures are in the ratio 4 : 3. If each saved ₹ 5,000, express the given situation algebraically as a system of linear equations in two variables. Hence, find their respective monthly incomes.

Answer 1

Let the monthly incomes of the two persons be 9x and 7x, and their monthly expenditures be 4y and 3y, respectively.

9x − 4y = 5000   ...(1)

7x − 3y = 5000   ...(2)

Multiply by 3 in equation (1) and by 4 in equation (2).

27x − 12y = 15000
28x − 12y = 20000
−    +         −           
−x = −5,000

x = 5,000

Monthly income of 1^st person = 9 × 5000

= 45,000

Monthly income of 2^nd person = 7 × 5000

= 35,000