The monthly incomes of two persons are in the ratio 5 : 4 and their monthly expenditures are in the ratio of 9 : 7. If each saves BDT 50 per month, what would be the total amount of their monthly expenditure?

Question: The monthly incomes of two persons are in the ratio 5 : 4 and their monthly expenditures are in the ratio of 9 : 7. If each saves BDT 50 per month, what would be the total amount of their monthly expenditure?

Solution:
Let,
Their monthly income 5a and 4a
Their monthly expenses 9b and 7b

ATQ,
5a - 9b = 50 ..............(1)
4a - 7b = 50 ...............(2)

Multiply equation (1) and (2) by 4 and 5 respectively,
20a - 36b = 200 .............(3)
20a - 35b = 250 ..............(4)

(3) - (4) ⇒
20a - 36b- 20a + 35b = 200 - 250
or, - b = - 50
∴ b = 50

Hence, their total monthly expenditure = 9 × 50 + 7 × 50 = 450 + 350 = 800 tk