The sum of the reciprocals of A’s ages (in years) 2 years ago and 2 years from now is. The present age of A is?

Answer: 4 years

Calculation:

Let, the present age of A = A

2 years ago, his age = A - 2

2 years from now, his age = A + 2

According to the question,

⇒ = 1/A - 2 + 1/A + 2 = 2/3

⇒ 3(A + 2 + A - 2) = 2(A + 2)(A - 2)

⇒ 6A = 2(A2 - 22)

⇒ A2 - 3A - 4 = 0

⇒ A2 + A - 4A - 4 = 0

⇒ A(A + 1) - 4(A + 1) = 0

⇒ (A - 4)(A + 1) = 0

⇒ A = 4 or -1

Since, age can't be negative A = 4

∴ The present age of A is 4 years.

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