Question

The monthly incomes of A and B are in the ratio 5:4 and their monthly expenditures are in the ratio 7:5.If each saves Rs.9000 per month,find the monthly income of each.

Answer 1

Let monthly income of A = x
monthly income of B = y

let expenditure of A = 7y
expenditure of B = 5x

let income of A = 5y
income of B = 4x

according to statement
5x - 7y = 9000 ...... (1)
4x - 5y = 9000 ...... (2)

(5x - 7y = 9000 )*4
(4x - 5y = 9000 )*5

20x - 28y = 36000.......(3)
20x - 25y = 45000.......(4)
equ(4)-equ(3)
0 +3y =9000
y = 3000
put the value of y in equation (1)
then
5x-7y=9000
5x-21000=9000
5x=30000
x=6000
so
the monthly income of A and B respectively 6000 and 3000