Question

The annual incomes of A and B are in the ratio 3 : 4 and their annual expenditure are in the ratio 5 : 7. If each Rs. 5000; find their annual incomes.

Answer 1

Let A’s annual in come = Rs.x
and B’s annual income = Rs. y

According to the question,
`x/y = 3/4`
4x - 3y = 0                   ...(1)
and,
`[ x - 5000 ]/[ y - 5000 ] = 5/7`
7x - 5y = 10000            ...(2)

Multiplying equation no. (1) by 7 and (2) by 4.
28x - 21y = 0                ....(3)
28x - 20y = 40,000       .....(4)

Subtracting equation (4) from (3)
     28x - 21y = 0
-   28x - 20y = 40,000 
    -      +         -           
            - y = - 40,000
              y = 40,000

From (1)
4x - 3(40,000) = 0
x = 30,000
Thus, A’s income in Rs. 30,000 and B’s income is Rs. 40,000.