Multiple choice

Rohan's mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. Find Rohan's present age.

  1. $12$ years
  2. $6$ years
  3. $10$ years
  4. $7$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Rohan's age be x. Mother's age is x + 26. In 3 years, ages are x + 3 and x + 29. (x + 3)(x + 29) = 360 => x^2 + 32x + 87 = 360 => x^2 + 32x - 273 = 0. Factoring gives (x + 39)(x - 7) = 0. So x = 7.

AI explanation

Let Rohan's present age be R, so his mother's age is R + 26. Three years from now, their ages will be R + 3 and R + 29, and the product is 360. The equation is (R + 3)(R + 29) = 360, which simplifies to R^2 + 32R + 87 = 360. Solving this quadratic equation yields R = 7. Rohan is 7 years old.

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