Multiple choice

The ratio of the ages of P and Q seven years ago was (3: 4) respectively. The ratio of their ages nine years from now will be (7: 8) respectively. What is Q's age after 14 years?

  1. 37 years

  2. 33 years

  3. 42 years

  4. 27 years
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A Correct answer
Explanation

Let ages 7 years ago be 3x and 4x. Current ages are 3x+7 and 4x+7. After 9 years: (3x+16)/(4x+16) = 7/8. Cross-multiplying: 24x+128 = 28x+112 → 4x = 16 → x = 4. Q's current age = 4×4+7 = 23. After 14 years: 23+14 = 37 years.

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