Divide 50 into two parts so that the sum of their reciprocals

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Divide 50 into two parts so that the sum of their reciprocals is 1/12 ?

1. 20, 30
2. 24, 26
3. 28, 22
4. 36, 14

Correct Option: A

Let the number be N and (50 - N)
Then, 1/N + 1/(50-N) = 1/12
⇒ (50 - N + N) / {N(50 - N)} = 1/12
⇒ N² - 50N + 600 = 0
⇒ N = 30 or 20
∴ the number are 20, 30