Question

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs 2000 per month, find their monthly incomes.

Answer 1

Let us denote the incomes of the two person by Rs 9x and Rs 7x and their expenditures by Rs 4y and Rs 3y respectively. Then the equations formed in the situation is given by :

9x – 4y = 2000 (1)

and 7x – 3y = 2000 (2)

Step 1: Multiply Equation (1) by 3 and Equation (2) by 4 to make the coefficients of y equal. Then we get the equations:

27x – 12y = 6000     .........(3)

28x – 12y = 8000   .........(4)

Step 2: Subtract Equation (3) from Equation (4) to eliminate y, because the coefficients of y are the same. So, we get

(28x – 27x) – (12y – 12y) = 8000 – 6000

i.e., x = 2000

Step 3: Substituting this value of x in (1), we get 

9(2000) – 4y = 2000

i.e., y = 4000

So, the solution of the equations is x = 2000, y = 4000. Therefore, the monthly incomes of the persons are Rs 18,000 and Rs 14,000, respectively.

Verification : 18000 : 14000 = 9 : 7. Also, the ratio of their expenditures =

18000 – 2000 : 14000 – 2000 = 16000 : 12000 = 4 : 3