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 A’s income.Solution
Let incomes be 2x and 3x. Let expenditures be 3y and 5y. Savings: Income − Expenditure For A: 2x − 3y = 1,000 …(1) For B: 3x − 5y = 500 …(2) Multiply (1) by 3: 6x − 9y = 3,000 Multiply (2) by 2: 6x −10y = 1,000 Subtract (2nd) from (1st): (6x − 9y) − (6x − 10y) = 3,000 − 1,000 y = 2,000 Substitute y = 2,000 in (1): 2x − 3×2,000 = 1,000 2x − 6,000 = 1,000 2x = 7,000 x = 3,500 A’s income = 2x = 2 × 3,500 = 7,000 Answer: A’s income = Rs 7,000.
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