A can complete a task in 30 days, and B can complete the same task in 40 days. They work together for 10 days, and then C joins them and completes the remaining work in 5 days. How long will C alone take to complete the task?
Show answer & explanation
Correct answer: C
Explanation
Given:
A = 30 days
B = 40 days
A and B = 10 days together
Remaining work A + B + C = 5 days
A's rate = 1/30
B's rate = 1/40
A + B's rate = 1/30 + 1/40 = 7/120
Work done in 10 days = 10 × 7/120 = 7/12
Remaining work = 1 − 7/12 = 5/12
(A + B + C) do 5/12 of the work in 5 days
1 day's work = (5/12) / 5 = 1/12
Rate of A + B + C = 1/12
Rate of C = 1/12 − 7/120 = 1/40
C's time alone = 40 days