Multiple choice

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

  1. 7

  2. 10

  3. 5

  4. 6
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A Correct answer
Explanation

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

AI explanation

Let Rehman's present age be x years, making his age 3 years ago x minus 3 and his age 5 years from now x plus 5. The given equation is 1 over (x minus 3) plus 1 over (x plus 5) equals 1 divided by 3. Finding the common denominator yields 2x plus 2 over the quantity (x minus 3)(x plus 5) equals 1 divided by 3, which simplifies to x squared minus 4x minus 21 equals 0. Solving this quadratic equation provides the roots x equals 7 or x equals negative 3, and discarding the negative age leaves Rehman's present age at 7 years.

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