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      Question

      The ratio of incomes of A and B is 3 : 5, and the ratio

      of their expenditures is 4 : 7. Each saves Rs 400 per month. Find their monthly incomes.
      A A’s income = Rs 4650; B’s income = Rs 2735 Correct Answer Incorrect Answer
      B A’s income = Rs 3600; B’s income = Rs 6000 Correct Answer Incorrect Answer
      C A’s income = Rs 3650; B’s income = Rs 6700 Correct Answer Incorrect Answer
      D A’s income = Rs 3670; B’s income = Rs 2000 Correct Answer Incorrect Answer

      Solution

      Let incomes: A = 3x, B = 5x Let expenditures: A = 4y, B = 7y Savings: 3x − 4y = 400 ...(1) 5x − 7y = 400 ...(2) Subtract (1) from (2): (5x − 7y) − (3x − 4y) = 400 − 400 2x − 3y = 0 2x = 3y ⇒ y = (2x)/3 Substitute into (1): 3x − 4(2x/3) = 400 3x − 8x/3 = 400 (9x − 8x)/3 = 400 x/3 = 400 x = 1200 Thus incomes: A = 3x = 3 × 1200 = 3600 B = 5x = 5 × 1200 = 6000 Answer: A’s income = Rs 3600; B’s income = Rs 6000.

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