Multiple choice

Three years ago and five years hence, the total of reciprocals of Rehman's age is $\dfrac{1}{3}$. What is the present age of Rehman?

  1. $5$
  2. $6$
  3. $7$
  4. $8$
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C Correct answer
Explanation

Let x be the present age. The equation is 1/(x-3) + 1/(x+5) = 1/3. Solving this, (x+5 + x-3) / (x^2 + 2x - 15) = 1/3, which leads to 3(2x + 2) = x^2 + 2x - 15. This simplifies to x^2 - 4x - 21 = 0, so (x-7)(x+3) = 0. Since age must be positive, x = 7.

AI explanation

Let Rehman's present age be x. The equation from the given word problem is 1/(x-3) + 1/(x+5) = 1/3. Combining the fractions gives (2x + 2) / (x^2 + 2x - 15) = 1/3, which cross-multiplies to x^2 - 4x - 21 = 0. Factoring this quadratic equation yields (x - 7)(x + 3) = 0, and since age must be positive, x is 7.

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