A can complete a piece of work in 8 hours, B can complete in 10 hours and C in…
2024
A can complete a piece of work in 8 hours, B can complete in 10 hours and C in 12 hours. If A, B, C start the work together but A leaves after 2 hours, find the time taken by B and C to complete the remaining work.
- A.
2(1/11)hrs
- B.
4(1/11)hrs
- C.
2(6/11)hrs
- D.
2 hrs
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept: For work-rate problems, take the total work as the LCM of the individual completion times so each person's rate becomes a whole number of units per hour. The combined rate of people working together is the sum of their individual rates, and work done in any period follows Work = Rate × Time; when someone leaves, the remaining work is finished at the rate of whoever continues.
Take total work = LCM(8, 10, 12) = 120 units.
A's rate = 120 ÷ 8 = 15 units/hour, B's rate = 120 ÷ 10 = 12 units/hour, C's rate = 120 ÷ 12 = 10 units/hour.
Combined rate of A, B and C working together = 15 + 12 + 10 = 37 units/hour.
Work completed by all three in the first 2 hours = 37 × 2 = 74 units.
Remaining work = 120 − 74 = 46 units.
After A leaves, B and C's combined rate = 12 + 10 = 22 units/hour.
Time taken by B and C to finish the remaining 46 units = 46 ÷ 22 = 23/11 = 2(1/11) hours.
Cross-check: In 2(1/11) hours, B and C together complete 22 × 23/11 = 46 units, exactly the leftover work, confirming the result.