Question

The sum reciprocal of ages of a person after 3years and 3years before is 8/45 Find his present age

Answer 1

Let the present age of the person be:

x years.

Then,

The age of the person:

After 3 years = (x+3) years

Before 3 years = (x-3) years

Now,

According to the question,

We have;

=> 1/(x+3) + 1/(x-3) = 8/45

=> {(x-3) + (x+3)}/(x+3)(x-3) = 8/45

=> 2x/(x^2 - 9) = 8/45

=> 2x•45 = 8•(x^2 - 9)

=> 45x = 4(x^2 - 9)

=> 45x = 4x^2 - 36

=> 4x^2 - 45x - 36 = 0

=> 4x^2 - 48x + 3x - 36 = 0

=> 4x(x - 12) + 3(x - 12) = 0

=> (x - 12)(4x + 3) = 0

=> x = 12 , x = - 3/4

Note that, the age can never be negative.

Thus, x = -3/4 is rejected.

Thus, the appropriate value of x is 12.

Hence, the present age of the person is 12 years.

Answer 2

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