Question
The ratio of incomes of A and B is 5:3, and their
expenditures are in the ratio 9:5. If A saves ₹800 and B saves ₹600, find B's income.Solution
ATQ, Incomes: A:B = 5:3 ⇒ A = 5x, B = 3x Expenditures: A:B = 9:5 ⇒ A = 9y, B = 5y Savings = Income − Expenditure A saves 800: 5x − 9y = 800 ...(1) B saves 600: 3x − 5y = 600 ...(2) Make x same: (1)×3: 15x − 27y = 2400 (2)×5: 15x − 25y = 3000 Subtract [(2)×5 − (1)×3]: (15x − 25y) − (15x − 27y) = 3000 − 2400 2y = 600 y = 300 Put y in (2): 3x − 5(300) = 600 3x − 1500 = 600 3x = 2100 B’s income = 3x = 2100
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