Question

sum of reciprocals of age of rehman 3 years ago and 6 years from now is 1/6.Find his present age

Answer 1

Let the present age of rehman be x years ;

Age of rehman 3 years ago = (x-3) years
and that of 6 years after = (x+6) years
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{1/(x-3)} + {1/(x+6)} = 1/6

{(x+6)+(x-3)} ÷ (x^2+6x-3x-18) = 1/6

6(2x+3) = x^2+3x-18
12x+18 = x^2 +3x -18

x^2 -9x-36 = 0
x^2+3x-12x-36 = 0
x(x+3) -12(x+3) = 0
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x = -3 & +12
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Hence the present age of rehman is 12 years.

Answer 2

Let the present age of Rehman be x
His age before 3yrs = x-3
His age after 6yrs = x+6
A/Q 1/x-3 + 1/x+6 = 1/6
x+6+x-3/x²+6x-3x-18 = 1/6
2x+3/x²+3x-18 = 1/6
12x+18 = x²+3x-18
x²-9x-36 = 0
x²-12x+3x-36 = 0
x(x-12)+3(x-12) = 0
(x+3)(x-12) = 0
If x+3 = 0
x = -3
Or If x-12 = 0
x = 12
Since, age cannot be negative,
∴ x = 12