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      Question

      The incomes of A and B are in the ratio 4 : 5 and their

      expenditures are in the ratio 7 : 9. If each saves Rs 4,000 per month, find B’s monthly income.
      A 40,500 Correct Answer Incorrect Answer
      B 40,000 Correct Answer Incorrect Answer
      C 48,000 Correct Answer Incorrect Answer
      D 61,000 Correct Answer Incorrect Answer

      Solution

      ATQ, Let A’s income = 4x, B’s income = 5x Let A’s expenditure = 7y, B’s expenditure = 9y Savings: For A: 4x − 7y = 4000 …(1) For B: 5x − 9y = 4000 …(2) Subtract (1) from (2): (5x − 9y) − (4x − 7y) = 0 x − 2y = 0 ⇒ x = 2y Substitute in (1): 4(2y) − 7y = 4000 8y − 7y = 4000 ⇒ y = 4000 Then x = 2y = 8000 B’s income = 5x = 5 × 8000 = 40,000.

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