A contractor undertakes to do a job within 20 days and hires

BTGmoderatorDC wrote:A contractor undertakes to do a job within 20 days and hires 60 people to do it. After 5 days, he realizes that one fifth of the work is done so he hires more people. How many more man he has to hire to complete the job in time?

1. 10
2. 12
3. 15
4. 20
5. 25

With the original crew of 60 people, 1/5 of the job was completed in 5 days. Thus, the rate of the 60 people is (1/5)/5 = 1/25.

We see that after 5 days, 4/5 of the job still needs to be completed in 15 days. Thus, the rate must be:

(4/5)/15 = 4/75

We can use the following proportion to determine how many people must be working together for a rate of 4/75:

60/(1/25) = x/(4/75)

1500 = 75x/4

6000 = 75x

80 = x

Thus, 20 more people must be hired.

Alternate Solution:

Since 60 workers did 1/5 of the job in 5 days, they would do the remaining 4/5 of the job in 4 x 5 = 20 days. We need the remaining job to be done in 15 days instead of 20, so let’s find the number of workers necessary to finish 4/5 of the job in 15 days using an inverse proportion: Let x denote the number of workers that would finish the remaining job in 15 days. Then,

60 * 20 = 15 * x

x = 4 * 20 = 80

Since 80 workers are needed to finish the remaining job in 15 days, 80 - 60 = 20 more workers must be hired.

Answer: D