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Question
The sum of the reciprocals of Varun's age (in years) 3 years ago and 5 years from now is `1/3`. Find his present age.
Solution
Let the varun's present age be x years
According to the question,
`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`
x2 + 2x – 15 = 6x + 6
x2 – 4x – 21 = 0
x2 – 7x + 3x – 21 = 0
x(x – 7) + 3(x – 7) = p
(x – 7)(x + 3) = 0
if x – 7 = 0, x = 7
if x + 3 = 0, x = – 3
Age can not be negative
∴ x = 7
Hence Varun's age be 7 years.
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