Multiple choice

The sum of the present ages of P and Q is 52 years. After 2 years Q’s age will be 2 years more than R’s age then. If P is younger than R by 6 years, find the age of Q 6 years ago.

  1. 20 years

  2. 22 years

  3. 24 years

  4. 25 years

  5. 28 years
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C Correct answer
Explanation

Let Q's present age be q and R's present age be r. The statement 'After 2 years Q's age will be 2 years more than R's age then' means q + 2 = (r + 2) + 2, which simplifies to q = r + 2. P is younger than R by 6 years, so p = r - 6. The sum of present ages of P and Q is 52, so p + q = 52. Substituting: (r - 6) + (r + 2) = 52, giving 2r - 4 = 52, so 2r = 56 and r = 28. Then q = r + 2 = 30. Q's age 6 years ago = 30 - 6 = 24 years.

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