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

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

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).

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

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).

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