Question
The incomes of A and B are in the ratio 4 : 5 and their
expenditures are in the ratio 3 : 4. Each of them saves Rs 2,000 per month. Find the monthly income of A.Solution
Let incomes be 4x and 5x. Let expenditures be 3y and 4y. Savings = Income − Expenditure For A: 4x − 3y = 2,000 …(1) For B: 5x − 4y = 2,000 …(2) Subtract (1) from (2): (5x − 4y) − (4x − 3y) = 0 x − y = 0 ⇒ x = y Substitute in (1): 4x − 3x = 2,000 ⇒ x = 2,000 So A’s income = 4x = 4 × 2,000 = Rs 8,000 Answer: Rs 8,000
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