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

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