Question
The incomes of A and B are in the ratio 4 : 5 and their expenditures are in the ratio 3 : 4. If each saves Rs 4,000, find the income of
B.
Solution
Let incomes: A = 4x, B = 5x Let expenditures: A = 3y, B = 4y Savings = Income − Expenditure For A: 4x − 3y = 4,000 …(1) For B: 5x − 4y = 4,000 …(2) Subtract (1) from (2): (5x − 4y) − (4x − 3y) = 0 5x − 4y − 4x + 3y = 0 x − y = 0 ⇒ x = y Substitute x = y in (1): 4x − 3x = 4,000 x = 4,000 So B’s income = 5x = 5 × 4,000 = Rs 20,000 Answer: Rs 20,000.
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