Question
The incomes of A and B are in the ratio 5 : 7 and their
expenditures are in the ratio 3 : 5. If each saves Rs 4,000, find the income of B.Solution
Let incomes be 5x and 7x. Let expenditures be 3y and 5y. Savings = Income − Expenditure For A: 5x − 3y = 4,000 …(1) For B: 7x − 5y = 4,000 …(2) Subtract (1) from (2): (7x − 5y) − (5x − 3y) = 0 7x − 5y − 5x + 3y = 0 2x − 2y = 0 ⇒ x = y Substitute x = y into (1): 5x − 3x = 4,000 2x = 4,000 ⇒ x = 2,000 Thus B’s income = 7x = 7 × 2,000 = Rs 14,000
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