A can complete a task in 10 days, while B can finish the same task in 12 days. They decide to work alternately, with A starting the work on the first day. How many days will it take for them to complete the entire task?
Show answer & explanation
Correct answer: C
Explanation
Given:
A works = 10 days
B works = 12 days
A starts work on the first day
A's rate per day = 1/10
B's rate per day = 1/12
Work done in 2 days = 1/10 + 1/12
= 6/60 + 5/60
= 11/60
Work done in 10 days (5 cycles) = 5 × 11/60 = 11/12
Remaining work = 1 − 11/12 = 1/12
A's rate = 1/10
Time = (1/12) ÷ (1/10) = 5/6 days
Total time = 10 + 5/6 = 10.83 days