Question

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

• A. Rs. 2000, Rs.4000
• B. Rs.3000, Rs.6000
• C. Rs. 4000, Rs.8000
• D. Rs. 4000, Rs. 6000.

Answer 1

The correct option is A Rs. 2000, Rs.4000

Let us denote the incomes of the two person by Rs 7x and Rs 5x and their expenditures by Rs 3y and Rs 2y respectively. Then the equations formed in the situation is given by :
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 (1), we get,
x = 2000 and y = 4000.
Therefore their monthly incomes are
Rs. 14,000 and Rs 10,000