A contract Is to be completed In 56 days and 104 men were set to work

Question

A contract must be completed in 56 days and 104 men are recruited to work, each working 8 hours a day. After 30 days, \(\frac{2}{5}\) of the work is finished. How many additional men must be employed so that the work is completed on time?

A. 180
B. 64
C. 76
D. 96
E. 120

A. 180 
B. 64 
C. 76 
D. 96 
E. 120

lucajava · Accepted Answer

Since 30 days are required to complete  \frac{2}{5}W , 75 are needed to complete  W .
30 days have already passed. Hence, 75-30 = 45 days are needed to complete  \frac{3}{5}W . Write down the following equation:

104 * 8 * 45 = \frac{3}{5}W

We seek the additional number of people to complete the remaining work in time. Since 30 days are left, 56 - 30 = 26 days only can be utilised. We can write:

x * 8 * 26 = \frac{3}{5}W

Solving this system of linear equations we get:

x = \frac{104*8*45}{8*26} = 180

Men should be employed to finish the job on time: 180 - 104 = 76.

effatara · Answer

Unitary method is the simplest and quickest way to solve this kind of problem:

TARGET: Find out how many men are needed to finish (3/5)th of the work in the remaining 26 days.

(2/5)W is done in 30 days by 104 men.
(3/5)W is done in 30 days by (104*5*3)/(2*5)=156 men
(3/5)W is done in 26 days by (156*30)/26=180 men.

Additional men to be hired: 180-104=76 Answer: C

ScottTargetTestPrep · Answer

The rate of 104 men is (2/5)/30 = 2/150 = 1/75. So we see that we need to complete 3/5 of the job in 26 days for a rate of:

(3/5)/26 = 3/130.

We can determine how many men must be used with the following proportion:

104/(1/75) = n/(3/130)

7,800 = 130n/3

23,400 = 130n

180 = n

Since they have 104 men already, they need 76 more men.

Alternate Solution:

If it took 104 men to complete 2/5 of the job in 30 days, then it would take the whole job

30/(2/5) = (30*5)/2 = 75

days to complete, without any additional men. Since we want the remaining job to be completed in 56 - 30 = 26 days instead of 75 - 30 = 45 days, we can find the number of men necessary by setting up an inverse proportion: It would take (104*45)/26 = 180 men to complete the remaining job in 26 days. Thus, 180 - 104 = 76 more men are needed.

Answer: C

GyanOne · Answer

Work done by 104 men working 8 hours a day in 30 days = 104*8*30 man hours
=> Work remaining at that point = (3/2)*104*8*30 = 45*8*104 man hours
=> If x additional men are deployed, then (104+x)*8*26 = 45*8*104
=> x = 76

Option (C).

GyanOne · Answer

Alternative solution 1: 
Note that the number of hours worked per man per day are not relevant here.

So, according to the question, 104 men working for 30 days complete 2/5 of the work. 
In how many days would these 104 men complete all of the work? In 30*(5/2) = 75 days. 
So, to complete (3/5) of the work in 56 days, we need (75*104/26)*(3/5) men, or 180 men. 
Thus, we need 76 additional men.

Option (C).

Alternative solution 2: 
Let k be the efficiency (work done per person per day) and W the total work. 
Then we have: 
104*30*8*k = (2/5)*W
AND
x*26*8*k=(3/5)*W

Dividing the equations, we get
x= 3*104*30/(2*26) = 180, or 76 additional men.

Option (C).

ScottTargetTestPrep · Answer

Notice that 1 - 2/5 = 3/5 of the job must be completed in 56 - 30 = 26 days.

Since 104 men complete 2/5 of the job in 30 days, they would complete 1/5 of the job in 15 days, and thus, they would complete 3/5 of the job in 3 x 15 = 45 days.

Let’s find the number of men necessary to complete the job (which would be completed by 104 men in 45 days) in 26 days. Let n be the number of men necessary to complete the job in 26 days. Notice that the number of men and the number of days is inversely proportional; thus we must have:

26n = 45 * 104

n = (45 * 104)/26 = 45 * 4 = 180

So, a total of 180 men must work on the job so that it is completed in 26 days. Since we already have 104 men, we need 180 - 104 = 76 additional men.

Answer: C

giovanni.ch92 · Answer

Can someone tell me if this approach is correct?

2/5 of work are done in 30days by 104men: 
2/5 = 104*rate*30
rate =    =

we need to do 3/5 of the work in 26days:
   = 26days*(104+x)*rate
   = 26*(  )
   = 104 + x
180 = 104 + x
x = 76

Thanks

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A contract Is to be completed In 56 days and 104 men were set to work

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