P can do a piece of work in 30 days and Q in 40 days. They work together for 4 days and then Q leaves. The number of days taken by P to finish the remaining work is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 23 days.
Let's first find their combined efficiency.
⇒ P's one day's work = 1/30 Q's one day's work = 1/40
⇒ So, their combined one day's work = 1/30 + 1/40 = 7/120
⇒ In 4 days, they complete 4 × (7/120) = 7/30 of the work.
⇒ Remaining work = 1 - 7/30 = 23/30
⇒ P alone can do 1/30 of the work in one day. So, he can do 23/30 of the work in (23/30) / (1/30) = 23 days.
Therefore, P will take 23 days to finish the remaining work.