Multiple choice

Aman's age is three times his son's age. Ten years ago his age was five times his son's age. Find their present ages.

  1. Aman's age: $90$ years; Aman's sons age: $30$ years
  2. Aman's age: $45$ years; Aman's sons age: $15$ years
  3. Aman's age: $60$ years; Aman's sons age: $20$ years
  4. Aman's age: $75$ years; Aman's sons age: $25$ years
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C Correct answer
Explanation

Let son's age be x, Aman's be 3x. 10 years ago: 3x - 10 = 5(x - 10). 3x - 10 = 5x - 50. 40 = 2x, so x = 20. Aman's age = 3 * 20 = 60.

AI explanation

Let the son's present age be $x$ years, making Aman's present age $3x$ years. Ten years ago, their ages were $x - 10$ and $3x - 10$, so the equation is $3x - 10 = 5(x - 10)$. Solving this gives $3x - 10 = 5x - 50$, which means $2x = 40$ and $x = 20$. Aman's son is 20 years old, and Aman is $3 \times 20 = 60$ years old.

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