P and Q working alone can complete a work in 5 days and 15 days respectively. They work on alternate days one at a time. P works on the first day. In how many days the whole work will be completed?
Show answer & explanation
Correct answer: B
Explanation
Given:
P's time = 5 days
Q's time = 15 days
P's work in 1 day = 1/5
Q's work in 1 day = 1/15
Work done in 2 days = 1/5 + 1/15 = 4/15
Work done in 4 days = 2 × (4/15) = 8/15
Work done in 6 days = 3 × (4/15) = 12/15
Remaining work = 1 − 12/15 = 3/15 = 1/5
On the 7th day, P will work.
P's work in 1 day = 1/5
Hence, the remaining work will be completed on the 7th day.