Multiple choice

The present ages of Manoj and Amit are in the ratio $2 : 3$. After $12$ years, their age will be in the ratio $11:15$. The present age of Amit is_____ .

  1. $32$ years
  2. $48$ years
  3. $40$ years
  4. $35$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let ages be 2x and 3x. (2x+12)/(3x+12) = 11/15. 15(2x+12) = 11(3x+12) => 30x + 180 = 33x + 132 => 3x = 48 => x = 16. Amit's age = 3x = 3 * 16 = 48.

AI explanation

Let the present ages of Manoj and Amit be 2x and 3x. After 12 years their ages will be 2x + 12 and 3x + 12, giving the proportion (2x + 12)/(3x + 12) = 11/15. Cross-multiplying yields 30x + 180 = 33x + 132, meaning 3x = 48. Amit's present age is 3x, which is 48 years.

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