The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 13 Find his present age.
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Let the present age of Rehman = x ∴ 3 years ago Rehman’s age = (x – 3) years 5 years later Rehman’s age = (x + 5) years Now, according to the condition,
1/(x – 3 ) + 1/(x + 5) = 1/3
(x + 5 + x – 3)/(x – 3)(x + 5) = 1/3
(2x + 2)/(x2 – 3x +5x – 15) = 1/3
x2 + 2x – 15 = 6x + 6
x2 – 4x – 21 = 0
(x + 3)(x – 7) = 0
Either, x + 3 = 0 Or, x – 7 = 0
Thus, x = 7 or – 3; but age cannot be negative.
Hence the present age of Rehman is 7 years.
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