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

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).

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.

Answer: C

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