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?
- 4 years
- 5 years
- 7 years
- None
Explanation
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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