M7MBA wrote: ↑

Sun Dec 27, 2020 3:37 pm

A group of 40 workers working together has to complete a piece of work in 30 days. If all the workers work at a constant rate and after 20 days, it was found that only the 14th of the work was completed, then how many more workers should be recruited so that the work gets completed on time?

A. 32
B. 100
C. 200
D. 240
E. 280

Answer: C

Solution:

If we let x = the rate of each worker per day, we can create the equation:

x * 40 * 20 = 1/4

800x = 1/4

x = 1/3200

Now, let n = the number of extra workers needed so that the remaining portion of the work (i.e., 3/4 of the work) can be completed in 30 - 20 = 10 more days. We can create the equation:

1/3200 * (40 + n) * 10 = 3/4

40 + n = 3/4 * 3200/10

40 + n = 240

n = 200

Alternate Solution:

Since 40 men can complete 1/4 of the job in 20 days, they can complete the entire job in 4 x 20 = 80 days. At this rate, the remaining 1 - 1/4 = 3/4 of the job can be completed in 80 * 3/4 = 60 days by the 40 men.

Notice that we need the job to be completed in 10 days instead of 60 days; i.e. 1/6 of the time. In order to achieve this, we need the number of men to be 6 times 40 men; i.e. 240 men. Since there are already 40 men working, an additional 240 - 40 = 200 men are required.

Answer: C