George can do a piece of work in 8 hours. Paul can do the same work in 10…
2024
George can do a piece of work in 8 hours. Paul can do the same work in 10 hours, Harry can do the same work in 12 hours. George, Paul and harry start the same work at 9 am, while George stops at 11 am, the remaining two complete the work. At what time will the work complete?
- A.
12.30 pm
- B.
11.30 am
- C.
01:05 pm
- D.
12 noon
Attempted by 821 students.
Show answer & explanation
Correct answer: C
Answer: 01:05 pm
Explanation and steps:
Rates per hour: George = 1/8, Paul = 1/10, Harry = 1/12.
Work done from 9:00 to 11:00 (2 hours) by all three = 2 * (1/8 + 1/10 + 1/12) = 37/60 of the job.
Remaining work after 11:00 = 1 - 37/60 = 23/60.
Combined rate of Paul and Harry = 1/10 + 1/12 = 11/60 per hour.
Time to finish remaining work = (23/60) ÷ (11/60) = 23/11 hours = 2 + 1/11 hours = 2 hours and 60/11 minutes.
Compute minutes and seconds: 1/11 hour = 60/11 minutes ≈ 5.4545 minutes = 5 minutes 27 seconds (approx). So the extra time ≈ 2 hours 5 minutes 27 seconds.
They reach 11:00 when George stops. Adding 2 hours 5 minutes 27 seconds gives finish time ≈ 1:05:27 pm, which is correctly reported as 01:05 pm.