Question

The sum of the reciprocal of Rehamens ages (in years) 3years ago and 5years from now that is 1/3. find his present age?

Answer 1

Let the age of Rehman 3 years ago be 'X'
His present age = X + 3
His age 5 years from now = X + 8

Given, Sum of reciprocal of his age 3 years ago and five years hence = 1/3
1/X + 1/X+8 = 1/3
X+8+X/(X*(X+8)) = 1/3
2X + 8/(X^2 + 8X) = 1/3
3*(2X + 8) = (X^2 + 8X)
6X + 24 = X^2 + 8X
X^2 + 2X - 24 = 0
X^2 + 6X - 4X - 24 = 0
X(X+6) - 4(X+6) = 0
(X-4)*(X+6) = 0
Hence, X = 4 [since age can't be negative, -6 is neglected]
X = 4years 3 years ago
Hence Present age = 4+ 3 = 7 years.
Hope it helps.

Answer 2

Answer:

Please refer the attachment dear