A and B can complete a work in 12 days, B and C can complete the same work in 15 days. A, B, and C together can complete the work in 10 days. How long will it take for A and C together to complete the work?
Show answer & explanation
Correct answer: C
Explanation
Given:
A + B = 12 days
B + C = 15 days
A + B + C = 10 days
A + B = 1/12
B + C = 1/15
A + B + C = 1/10
(A + C) = (A + B + C) − B
Find B first
B = (A + B) + (B + C) − (A + B + C)
B = 1/12 + 1/15 − 1/10
= (5 + 4 − 6)/60
= 3/60
= 1/20
Now
A + C = 1/10 − 1/20 = 1/20
Time = 20 days
A and C together will complete the work in 20 days.