Question
The incomes of A and B are in the ratio 2 : 3 and their
expenditures are in the ratio 3 : 5. If A saves Rs 1,000 and B saves Rs 500, find the income of B.Solution
Let incomes: A = 2k, B = 3k Let expenditures: A = 3m, B = 5m Savings: 2k − 3m = 1,000 …(1) 3k − 5m = 500 …(2) Multiply (1) by 3, (2) by 2: (1): 6k − 9m = 3,000 (2): 6k −10m = 1,000 Subtract (2) from (1): (6k − 9m) − (6k − 10m) = 3,000 − 1,000 m = 2,000 Now from (1): 2k − 3×2,000 = 1,000 2k − 6,000 = 1,000 2k = 7,000 k = 3,500 Income of B = 3k = 3 × 3,500 = 10,500 Answer: B’s income = Rs 10,500.
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