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

Let the two parts be x and 50 − x.

Given that the sum of their reciprocals is 1/12:

1/x + 1/(50 − x) = 1/12.

Combine the fractions:

(50 − x + x) / [x(50 − x)] = 1/12

50 / [x(50 − x)] = 1/12

So x(50 − x) = 600.

Expand and rearrange:

50x − x² = 600 ⇒ x² − 50x + 600 = 0.

Solve the quadratic:

x = [50 ± √(2500 − 2400)]/2 = [50 ± 10]/2.

Thus x = 20 or x = 30, giving the two parts as 20 and 30.