Multiple choice

The sum of the reciprocals of Amar's ages 3 years ago and 5 years from now is 1/3. The present age of Amar is:

  1. 5

  2. 6

  3. 7

  4. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the present age. 1/(x-3) + 1/(x+5) = 1/3. (x+5 + x-3) / ((x-3)(x+5)) = 1/3. (2x+2) / (x^2 + 2x - 15) = 1/3. 6x + 6 = x^2 + 2x - 15. x^2 - 4x - 21 = 0. (x-7)(x+3) = 0. x = 7.

AI explanation

Let Amar's present age be x years. The equation based on the given sum of reciprocals is 1 / (x - 3) + 1 / (x + 5) = 1 / 3. Simplifying the left side gives (2x + 2) / (x^2 + 2x - 15) = 1 / 3, and cross-multiplying yields x^2 - 4x - 21 = 0. Factoring this quadratic equation gives (x - 7)(x + 3) = 0, so the present age is 7 years.

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