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      Question

      The present ages of A and B are such that 8 years ago,

      the ratio of A’s age to B’s age was 7 : 5. Four years from now, the ratio of their ages will be 11 : 9. What is B’s present age?
      A 28 yrs Correct Answer Incorrect Answer
      B 25 yrs Correct Answer Incorrect Answer
      C 23 yrs Correct Answer Incorrect Answer
      D 17 yrs Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      Let present ages of A and B be a and b. Condition 1 (8 years ago): (a − 8) / (b − 8) = 7/5 ⇒ 5(a − 8) = 7(b − 8) ⇒ 5a − 40 = 7b − 56 ⇒ 5a − 7b = −16 …(i) Condition 2 (4 years hence): (a + 4) / (b + 4) = 11/9 ⇒ 9(a + 4) = 11(b + 4) ⇒ 9a + 36 = 11b + 44 ⇒ 9a − 11b = 8 …(ii) Solve (i) and (ii): Multiply (i) by 9: 45a − 63b = −144 Multiply (ii) by 5: 45a − 55b = 40 Subtract: (45a − 55b) − (45a − 63b) = 40 − (−144) 8b = 184 b = 23 So B’s present age = 23 years.

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