50 is divided into two parts such that the sum of their reciprocals is 1/12. Find the two parts.
A
30 and 20
B
30 and 25
C
30 and 40
D
30 and 35
Correct Answer: 30 and 20
Hints: Look at the answer, only A has 30 and 20, 30 + 20 = 50, which is the answer. Alternatively, let the two parts be x, y ; so x + y = 50 1/x + 1/y = 1/12 (y + x)/xy = 1/12 50 /xy = 1/12 xy = 600 x( 50 - x) = 600 50x - x2 = 600 x2 - 50x + 600 = 0 (x - 30) (x - 20) = 0 x = 30, 20