A group of 30 employees working 4 hours a day can complete a project in 10 days. What is the number of days in which

Mikrislac wrote: ↑

Sun Jul 26, 2020 2:03 am

A group of 30 employees working 4 hours a day can complete a project in 10 days. What is the number of days in which another group of 45 employees working 8 hours a day can complete twice the amount of work of the previous group? Assume that 2 employees of the first group can do as much work in 2 hours as can 4 employees of the second group in one hour.

A. 3 and 1/3 days
B. 3 and 1/6 days
C. 5 and 5/6 days
D. 6 and 2/3 days
D. 7 and 3/5 days

Solution:

If 2 employees of the first group can do as much work in 2 hours as can 4 employees of the second group in one hour, then the hourly rate of each person in the first group is the same as the hourly rate of each person in the second group.
For the first group which has 30 employees working 4 hours a day can complete a project in 10 days. If they work 20 days, they will complete twice the amount of work, i.e., two projects. If they double the number of hours they work each day while halving the number of employees, they will complete the project or projects in the same number of days. That is, 15 employees working 8 hours a day can complete two projects in 20 days.
Now, let’s look at the second group, it has 45 employees working 8 hours a day and we need to determine the number of days they can complete two projects. Recall that if the first group has15 employees working 8 hours a day, they can complete two projects in 20 days. Since the second group has 3 times as many employees working the same number of hours a day, it must be true that they can complete the two projects in one-third of the time, i.e., in 20 x 1/3 = 20/3 = 6 ⅔ days.

Alternate Solution:

The number of worker-hour-days for the first group to complete the entire project is 30 x 4 x 10 = 1200.
Since 2 x 2 = 4 x 1, we see that the second group’s workers work at the same pace as the first group’s workers.
We are told that the second group will do twice as much work as the first group. Thus, the second group will require 1200 x 2 = 2400 worker-hour-days to perform their project. If we let x = the number of days required for the second group, we have:
x = 2400/(45 * 8)
x = 2400/360
x = 20/3 = 6 ⅔ days

Answer: D