50 is divided into two parts such that the sum of their reciprocals is 1/12. Find the two parts.

Answer: A. 20, 30

Let the parts be x and 50 - x. 1/x + 1/(50 - x) = 1/12 gives 50/(x(50 - x)) = 1/12, so x(50 - x) = 600 and x² - 50x + 600 = 0.
(x - 20)(x - 30) = 0, so the parts are 20 and 30.

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