Question

the sum of the reciprocal of rahman's age (in years ) 3 year ago and 5 year from now is 1/3 .find his present age .​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the present age of rahman be x years.

Rahman's age 3 years ago = (x - 3) years.

Rahman's age 5 years hence = (x + 5) years.

According to the Question,

⇒ 1/(x - 3) + 1/(x + 5) = 1/3

⇒ (x + 5) + (x - 3)/(x - 3) (x + 5) = 1/3

⇒ (x - 3) (x + 5) = 6(x + 1)

⇒ x² + 2x - 15 = 6x + 6

⇒ x² - 4x - 21 = 0

⇒ x² - 7x + 3x - 21 = 0

⇒ x(x - 7) + 3(x - 7) = 0

⇒ (x - 7) (x + 3) = 0

⇒ x - 7 = 0 or x + 3 = 0

⇒ x = 7, - 3 (As x can't be negative)

⇒ x = 7

Hence, the present age of rahman is 7 years.

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