Multiple choice

Six years ago, the ratio of the ages of the two persons P and Q was 3 : 2. Four years hence, the ratio of their ages will be 8 : 7. What is P's present age?

  1. 10 years

  2. 12 years

  3. 14 years

  4. 8 years

  5. Na
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let ages 6 years ago be 3x and 2x. Present ages are 3x+6 and 2x+6. Four years hence, ages will be 3x+10 and 2x+10. (3x+10)/(2x+10) = 8/7. 21x + 70 = 16x + 80, so 5x = 10, x = 2. P's present age = 3(2) + 6 = 12.

AI explanation

Let their present ages be P and Q. Six years ago, (P - 6) / (Q - 6) = 3/2, and four years hence, (P + 4) / (Q + 4) = 8/7. Cross-multiplying yields 2P - 3Q = -6 and 7P - 8Q = -4. Solving this system of equations gives Q = 10 and P = 12, so P's present age is 12 years.

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