Question

The ratio of the income of two persons is 7:5 and the ratio of their expenditure is 3:2. If each of them manages to save Rs 2000 per month, find their monthly income.

Answer 1

Let us denote the income of the two persons by Rs 7x and Rs 5x and their expenditure by Rs 3y and Rs 2y respectively.
Then the equations formed according to the given conditions are,

7x – 3y = 2000...(1)
and 5x – 2y = 2000...(2)

Multiply equation (1) by 2 and equation (2) by 3 to make the coefficients of y equal. Then, we get the equations:

14x – 6y = 4000...(3)
15x – 6y = 6000...(4)

Subtract equation (3) from equation (4) to eliminate y, because the coefficients of y are the same. So, we get

(15x – 14x) – (6y – 6y) = 6000 – 4000
i.e., x = 2000

Substituting this value of x in equation (1), we get,

7(2000) - 3y = 2000
3y = 14000 - 2000
i.e., y = 4000

Therefore, the monthly income of the given two persons are
Rs. 14,000 and Rs 10,000, respectively.