A Contract is to be Completed in 46 days and 117 Men Were set to Work, each Working 8 hours a Day GMAT Problem Solving

Question: A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, (4/7) of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours?

(A) 80
(B) 81
(C) 82
(D) 83
(E) 84

Correct Answer: B

Solution and Explanation:
Approach Solution 1:

This question has only one approach
The given condition in a contract states that it is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, (4/7) of the work is completed. Accordingly, it is to find the number of additional men who may be employed so that the work may be completed in time, with each man now working 9 hours. Let the total man-hours may be assumed to be x.

Based on the given situation, after 33 days, 4/7th of the work is said to be completed. Accordingly, if it is assumed that each worker works 1unit of work in one hour, then in 33 days, 117*8*33 hours of work are completed.

By assuming that the total man hours as x, the man-hours completed after 33 days implicating 4/7th of the work can be equated as follows:

\(\rightarrow\frac{4x}{7}=117*8*33\)

\(\rightarrow x=117*7*8*33\)

\(\rightarrow x=117*7*33*2 \) man hours

In order to complete the given contract of work in time, it is important to employ an additional number of men as given in the condition. Accordingly, it evaluates that with an additional number of men each worker to complete the work in time would need to work 9 hours. This implies that the additional man hours left for the completion of the task is as follows:

= 117∗7∗33∗2−117∗8∗33

= 117∗33∗(14−8)

= 117∗33∗6 man hours

Hence, 117∗33∗6 man hours is left for the entire contract to be completed.

Considering that the contract is for 46 days and 33 days of work is already complete, the number of days left to complete the contract is 13days.

With this, let the total number of men required for work of completing the contract be m. To find the number of additional men required, the following can be resolved:

m∗9∗13=117∗33∗6

\(\rightarrow m=\frac{117*33*6}{9*13}=198\)

Accordingly, the total number of men to be working for the contract is 198. However, the number of additional men to be working can be subtracted from the total number of men who are supposed to work. This implies 198 with the number of men who have completed 4/7th of the task which is 117. This implies-

198 - 117 = 81.

Thus, the additional number of men required for the contract to be completed with workers at 9 hours of work for the next 13 days is 81. 

“A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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