P and Q alone can do a work in 18 and 45 days respectively. They started the…
2021
P and Q alone can do a work in 18 and 45 days respectively. They started the work together and P left after 3 days of start of work. Q completed the remaining work. In how many days was the work completed?
- A.
37.5
- B.
39.5
- C.
34
- D.
36
Attempted by 59 students.
Show answer & explanation
Correct answer: A
Solution:
P's rate = 1/18 of the work per day. Q's rate = 1/45 of the work per day.
Combined rate = 1/18 + 1/45 = 7/90 of the work per day.
Work done in the first 3 days = 3 × 7/90 = 7/30 of the work.
Remaining work = 1 - 7/30 = 23/30 of the work.
Time for Q alone to finish remaining work = (23/30) ÷ (1/45) = (23/30) × 45 = 34.5 days.
Total time = initial 3 days + 34.5 days = 37.5 days.
Answer: 37.5 days.