A and B can do a piece of work in 25 days and 30 days, respectively. They worked together for 6 days, after while B was replaced by P and the work was finished in the next 8 days. How long will P alone take to complete the same work?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. days.
A's rate = 1/25, B's rate = 1/30
Work done in 6 days by A and B = 6 × (1/25 + 1/30) = 22/50
Remaining work = 1 - 22/50 = 14/25
A and P together finish remaining in 8 days:
8 × (1/25 + P's rate) = 14/25
(1/25 + P's rate) = 14/200 = 7/100
P's rate = 7/100 - 1/25 = 3/100
Time by P alone = 1 / (3/100) = 100/3 = 33⅓ days