George can do a piece of work in 8 hours. Paul can do the same work in 10…

2026

George can do a piece of work in 8 hours. Paul can do the same work in 10 hours, Hari can do the same work in 12 hours. George, paul and hari start the same work at 9 am, while george stops at 11 am, the remaining two complete the work. What time will the work complete?

  1. A.

    11.30 am

  2. B.

    12 noon

  3. C.

    12.30 pm

  4. D.

    1 pm

Attempted by 1964 students.

Show answer & explanation

Correct answer: D

Correct approach and calculation:

  1. Choose a convenient total work: 120 units (LCM of 8, 10, 12).

  2. Compute individual rates: George = 120/8 = 15 units/hr, Paul = 120/10 = 12 units/hr, Hari = 120/12 = 10 units/hr.

  3. Work done from 9:00 to 11:00 (2 hours) by all three = 2 × (15 + 12 + 10) = 2 × 37 = 74 units.

  4. Remaining work = 120 − 74 = 46 units.

  5. Paul and Hari together do 12 + 10 = 22 units/hr. Time to finish the remaining 46 units = 46/22 = 2.090909… hours = 2 hours + 1/11 hour.

  6. Convert 1/11 hour to minutes: (60/11) ≈ 5.4545 minutes = 5 minutes 27 seconds (approximately).

  7. So the work finishes at 11:00 + 2 hours 5 minutes 27 seconds ≈ 1:05:27 pm (approximately 1:05 pm).

  8. Note: None of the given options (11:30 am, 12:00 noon, 12:30 pm, 1:00 pm) exactly match this result. The closest option is 1:00 pm, but it is about 5 minutes earlier than the precise completion time.

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