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Tom, Amanda and Harry working alone can finish a task in 4, 6, and 12
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10 Jun 2025, 23:45
10 Jun 2025, 23:45
Expert Reply
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Question Stats:
83% (03:48) correct
16% (02:26) wrong based on 6 sessions
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Tom, Amanda and Harry working alone can finish a task in 4, 6, and 12 hours respectively. Tom, Amanda and Harry start working together and work for 1 hour, then Tom leaves and Amanda and Harry work together for 1 hour, then Amanda leaves and the rest of the work is done by Harry alone. If the task was started at 10.00 am, then at what time does the task get completed?
(A) $\(12: 00 \mathrm{pm}\)$
(B) $\(12: 30 \mathrm{pm}\)$
(C) $\(3: 00 \mathrm{pm}\)$
(D) $\(4: 00 \mathrm{pm}\)$
(D) $\(4: 40 \mathrm{pm}\)$
(A) $\(12: 00 \mathrm{pm}\)$
(B) $\(12: 30 \mathrm{pm}\)$
(C) $\(3: 00 \mathrm{pm}\)$
(D) $\(4: 00 \mathrm{pm}\)$
(D) $\(4: 40 \mathrm{pm}\)$
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Re: Tom, Amanda and Harry working alone can finish a task in 4, 6, and 12
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13 Jun 2025, 04:00
13 Jun 2025, 04:00
Expert Reply
- Tom: Finishes the task in 4 hours. In 1 hour, Tom completes $\(1 / 4\)$ of the task.
- Amanda: Finishes the task in 6 hours. In 1 hour, Amanda completes $\(1 / 6\)$ of the task.
- Harry: Finishes the task in 12 hours. In 1 hour, Harry completes $\(1 / 12\)$ of the task.
First 1 hour (Tom, Amanda, and Harry working together):
- Work done $\(=(1 / 4)+(1 / 6)+(1 / 12)=(3 / 12)+(2 / 12)+(1 / 12)=6 / 12=1 / 2\)$.
- Remaining work $\(=1-(1 / 2)=1 / 2\)$.
Next 1 hour (Amanda and Harry working together):
- Work done $\(=(1 / 6)+(1 / 12)=(2 / 12)+(1 / 12)=3 / 12=1 / 4\)$.
- Remaining work $\(=(1 / 2)-(1 / 4)=1 / 4\)$.
Harry alone:
- Harry completes $\(1 / 12\)$ of the work in 1 hour.
- Time for Harry to complete the remaining $1 / 4$ of the work: $\((1 / 4) /(1 / 12)=(1 / 4) * 12=3\)$ hours.
Total time:
- 1 hour (all three) +1 hour (Amanda and Harry) +3 hours (Harry alone) $=5$ hours.
Start time: 10:00 am
Finish time: 10:00 am +5 hours $=3: 00 \mathrm{pm}$.
- Amanda: Finishes the task in 6 hours. In 1 hour, Amanda completes $\(1 / 6\)$ of the task.
- Harry: Finishes the task in 12 hours. In 1 hour, Harry completes $\(1 / 12\)$ of the task.
First 1 hour (Tom, Amanda, and Harry working together):
- Work done $\(=(1 / 4)+(1 / 6)+(1 / 12)=(3 / 12)+(2 / 12)+(1 / 12)=6 / 12=1 / 2\)$.
- Remaining work $\(=1-(1 / 2)=1 / 2\)$.
Next 1 hour (Amanda and Harry working together):
- Work done $\(=(1 / 6)+(1 / 12)=(2 / 12)+(1 / 12)=3 / 12=1 / 4\)$.
- Remaining work $\(=(1 / 2)-(1 / 4)=1 / 4\)$.
Harry alone:
- Harry completes $\(1 / 12\)$ of the work in 1 hour.
- Time for Harry to complete the remaining $1 / 4$ of the work: $\((1 / 4) /(1 / 12)=(1 / 4) * 12=3\)$ hours.
Total time:
- 1 hour (all three) +1 hour (Amanda and Harry) +3 hours (Harry alone) $=5$ hours.
Start time: 10:00 am
Finish time: 10:00 am +5 hours $=3: 00 \mathrm{pm}$.
gmatclubot
Re: Tom, Amanda and Harry working alone can finish a task in 4, 6, and 12 [#permalink]
13 Jun 2025, 04:00
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