A and B together can complete a work in 12 days. B and C together can complete it in 15 days. C and A together in 20 days. How many days will each take working alone?
Show answer & explanation
Correct answer: A
Explanation
Given:
A + B = 12 days
B + C = 15 days
C + A = 20 days
A + B = 1/12
B + C = 1/15
C + A = 1/20
(A + B) + (B + C) + (C + A) = 1/12 + 1/15 + 1/20 = 1/5
2(A + B + C) = 1/5
A + B + C = 1/10
A = (A + B + C) − (B + C)
A = 1/10 − 1/15
= (3 − 2) / 30
= 1/30
A's time = 30 days
B = (A + B + C) − (C + A)
B = 1/10 − 1/20
= (2 − 1) / 20
= 1/20
B's time = 20 days
C = (A + B + C) − (A + B)
C = 1/10 − 1/12
= (6 − 5) / 60
= 1/60
C's time = 60 days
A = 30 days
B = 20 days
C = 60 days