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# Twelve engineers can complete a task in 7 Hours. Twelve engineers star

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Joined: 02 Sep 2009
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Twelve engineers can complete a task in 7 Hours. Twelve engineers star  [#permalink]

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06 Nov 2019, 06:53
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:35) correct 33% (02:38) wrong based on 51 sessions

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Twelve engineers can complete a task in 7 Hours. Twelve engineers started the task at 10 am but starting from 1 pm, one engineer leaves every hour. At what time the task gets completed?

A. 5.30 pm
B. 6.00 pm
C. 6.30 pm
D. 7.00 pm
E. 7.30 pm

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Joined: 19 Oct 2018
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Re: Twelve engineers can complete a task in 7 Hours. Twelve engineers star  [#permalink]

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06 Nov 2019, 07:36
1
Assume 1 engineer can do 1 unit of work per hour

Total amount of work= 12*7=84 units

Work finished until 1PM= 12*3=36
Remaining work= 84-36=48

Amount of work finished from 1 to 6= 11+10+9+8+7=45

Time taken to finish remaining work=$$\frac{(48-45)}{6}$$= $$\frac{1}{2}$$ hour

Task gets completed at 6:30 PM

Bunuel wrote:
Twelve engineers can complete a task in 7 Hours. Twelve engineers started the task at 10 am but starting from 1 pm, one engineer leaves every hour. At what time the task gets completed?

A. 5.30 pm
B. 6.00 pm
C. 6.30 pm
D. 7.00 pm
E. 7.30 pm

Are You Up For the Challenge: 700 Level Questions
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Joined: 18 Aug 2017
Posts: 5738
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Twelve engineers can complete a task in 7 Hours. Twelve engineers star  [#permalink]

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06 Nov 2019, 09:42
1
total work= 7*12 ; 84 units
for 10 am to 1 pm total work done ; 12*3 ; 36 units
left 84-36 ; 48 units
this 48 unit of work can be completed from 1 pm onwards by 11+10+9+8+7 ; 45 units and 3 units of work can be done in 3/6 ; 1/2 hour
total time of work shall be completed by 6:30 PM
IMO C

Bunuel wrote:
Twelve engineers can complete a task in 7 Hours. Twelve engineers started the task at 10 am but starting from 1 pm, one engineer leaves every hour. At what time the task gets completed?

A. 5.30 pm
B. 6.00 pm
C. 6.30 pm
D. 7.00 pm
E. 7.30 pm

Are You Up For the Challenge: 700 Level Questions
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Joined: 24 Jul 2011
Posts: 1917
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: Twelve engineers can complete a task in 7 Hours. Twelve engineers star  [#permalink]

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06 Nov 2019, 11:22
Top Contributor
Bunuel wrote:
Twelve engineers can complete a task in 7 Hours. Twelve engineers started the task at 10 am but starting from 1 pm, one engineer leaves every hour. At what time the task gets completed?

A. 5.30 pm
B. 6.00 pm
C. 6.30 pm
D. 7.00 pm
E. 7.30 pm

Are You Up For the Challenge: 700 Level Questions

Let us assume that every engineer does 1 unit of work in 1 hour.

If nobody had left, they would have completed the work at 5 sharp (i.e. in 7 hours from 10am).

Since one engineer leaves every hour, 1+2+3+4 units of work (or 10 units of work) is still left by 5pm. Number of engineers left at 5pm = 7.

In the next hour, they will complete 7 units of these 10 units. At 6pm, 3 units are left, and 6 engineers are left to complete them. They will do so in half an hour.

So the work will be complete at 6:30.

Option (C).
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Re: Twelve engineers can complete a task in 7 Hours. Twelve engineers star  [#permalink]

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07 Nov 2019, 20:01
Bunuel wrote:
Twelve engineers can complete a task in 7 Hours. Twelve engineers started the task at 10 am but starting from 1 pm, one engineer leaves every hour. At what time the task gets completed?

A. 5.30 pm
B. 6.00 pm
C. 6.30 pm
D. 7.00 pm
E. 7.30 pm

Are You Up For the Challenge: 700 Level Questions

Since the rate for 12 engineers is 1/7, after 3 hours of work (from 10 am to 1 am), 3 x 1/7 = 3/7 of the job had been completed and therefore 4/7 of the job is left to be completed.

Furthermore, the rate of 1 engineer is (1/7)/12 = 1/84, so the rate of 11 engineers is 11/84.

So, by 2 pm, 4/7 - 11/84 = 48/84 - 11/84 = 37/84 of the job is left to be completed.

The rate for 10 engineers is 10/84.

So, by 3 pm, 37/84 - 10/84 = 27/84 of the job is left to be completed.

The rate for 9 engineers is 9/84.

So, by 4 pm, 27/84 - 9/84 = 18/84 of the job is left to be completed

The rate for 8 engineers is 8/84.

So, by 5 pm, 18/84 - 8/84 = 10/84 of the job is left to be completed.

The rate for 7 engineers is 7/84.

So, by 6 pm, 10/84 - 7/84 = 3/84 of the job is left to be completed.

The rate of 6 engineers is 6/84.

So, by 6:30 pm, 3/84 - 1/2 x 6/84 = 0 of the job is left to be completed. That is, the job will be completed by 6:30 pm.

Alternate Solution:

Since it takes 12 engineers 7 hours to do the job, the total job can be accomplished in 84 hours.

From 10 - 1, we have 12 x 3 = 36 hours of work accomplished.

From 1 - 2, we have 11 additional hours, for a total of 36 + 11 = 47 hours.

From 2 - 3, we have 10 additional hours, for a total of 47 + 10 = 57 hours.

From 3 - 4, we have 9 additional hours, for a total of 57 + 9 = 66 hours.

From 4 - 5, we have 8 additional hours, for a total of 66 + 8 = 74 hours.

From 5 - 6, we have 7 additional hours, for a total of 74 + 7 = 81 hours.

Since the entire job requires 84 hours, we need only 3 more hours of work, which can be accomplished by the 6 remaining engineers in half an hour. Thus, the job will be completed at 6:30 pm.

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Re: Twelve engineers can complete a task in 7 Hours. Twelve engineers star   [#permalink] 07 Nov 2019, 20:01
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