A contractor was hired to complete a certain construction job in 80

Question

A contractor was hired to complete a certain construction job in 80 days. To meet this deadline, the contractor initially assigns 120 men, each working 10 hours per day at a constant rate. After 40 days with these 120 men, an inspection shows that only 3/8 of the job has been completed. At that point, how many additional men, working at the same rate and for 10 hours per day, must be hired to finish the job on time?

(A) 50
(B) 60
(C) 70
(D) 80
(E) 90

(A) 50
(B) 60
(C) 70
(D) 80
(E) 90

M47-17

Bunuel · Accepted Answer

GMAT Club Official Solution:

Work done in first 40 days = 120 * 40 * 10 = 48,000 man-hours.

This equals 3/8 of the total work, so total work = 48,000/(3/8) = 128,000 man-hours.

Remaining work = 128,000 - 48,000 = 80,000 man-hours.

Time left = 80 - 40 = 40 days, so each man can do 40 * 10 = 400 man-hours.

Men needed for remaining work = 80,000/400 = 200.

Additional men needed = 200 - 120 = 80.

Answer: D.

obedear · Answer

This one took me nearly 3 mins to solve algebraically, including setting up my equations. Curious if anyone knows a better logical way. 
First, let's find the rate of a single man on the job, let R equal the rate of 1 man. Create an equation using R * T = W. 
120*R*40=3/8.

Solving for R, we get R = 1/1600*8.

Now that we know the rate of one construction worker, we can create an equation to solve directly for what the question is asking for.

Let x equal the number of additional men beyond 120 needed to complete the remaining 5/8ths of the job in 40 days.

(120 + x)*1/1600*8*40=5/8.

Always a good reminder to simplify before you multiply.

In this case, we have (120+x)/40*8 = 5/8.
120+x/320 = 5/8
960+8x = 1600
8x = 640
x = 80.

Answer D.

Notice that I ignored the 10 hours per day part when setting up my equation as since the additional men are all working the same number of hours per day it does not change the basic rate of the working men.

Dereno · Answer

The question mentions a deadline date was fixed before starting the work.

So, to meet the deadline. The contractor assigns 120 men, each working for 10 hours per day, at a constant rate.

So after 40 days, the inspection of work is done.

120 * 40 * 10 * rate = (3/8) of the total job.

Total job = (8*120*40*10)/3 = 128000.

So we need to complete the work on time, which means the number of days left is 80-40 = 40 days.

With this rate , we can finish another (3/8) of the work. So, we hire additional workforce. Let that be w.

(120+w) * 40 * 10 = (5/8)* (128000)

(120+w) * 40 * 10 = 80,000

120+W = 200

w = 80

so, additional work force needed is  80.

Option D

rajatsahu · Answer

Work done in the first 40 days
Men = 120
Hours/day = 10
Days worked = 40
Total man-hours used so far: 120×10×40=48,000 (This completes 3/8 of the job)

If 48,000 man-hours = 3/8 of the job, then total work is: 48,000×8/3=128,000 man-hours
Work left = 128,000−48,000=80,000 man-hours
Time remaining = 80-40 days = 40 days

Each man works: 10×40=400 hours
So required number of men:80,000 / 400= 200 men

We already have 120 men , so required men: 200 - 120 = 80 men ( option D )

A contractor was hired to complete a certain construction job in 80

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A contractor was hired to complete a certain construction job in 80

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