A manager hired 4 employees to complete a certain project in 15 days.

4 workers have completed the first half of the project in 10 days
in half that time, 5 days, twice as many workers will complete the second half
4
D

4 Employees completed half work in 10 days so rate of each employee is equal to
10 days*4(Rate of one employee)= 1/2, Rate of one employee = 1/80, given we have to complete 1/2 work in 5 days with each employee working at 1/80 rate , lets calculate how many employees required in total
5 days* x employees(1/80)=1/2.............. solving this we get x=8 so total 8 employees would be require to complete work we already have 4 hired so new requirement is 4 additional employees

Hi..

Just another way

How many mandays was expected 4*15=60
What has already been spent 4*10=40 to do half work so actual mandays required = 40*2=80...
So remaining work has to be done in 60-40 =20, which otherwise would get over in 80-40=40, double of 20 days..
So ofcourse you require double the person to complete the work, otherwise being done in double the time... So double the manpower =2*4=8
Extra manpower requirement =8-4=4

ALTER THE STANDARD RT=W FORMULA A BIT

Add (# of workers) to the standard formula (R*T=W).

That is, write it as (#)*R*T=W, or W=(#)*R*T. Manipulate that formula in the same way as RT=W

FIRST PHASE OF WORK - find individual rate. From that you can find # of workers for the second phase.

W = (# of workers) * r * t
W = \(\frac{1}{2}\)
# of workers = 4
r = ??
Time = 10 days

W = (#)*r*t
\(\frac{1}{2} = 4 * r * 10\)
\(r = \frac{(\frac{1}{2})}{4*10}=\frac{(\frac{1}{2})}{40}=\frac{1}{80}\)

At that individual rate, how many [more] workers are needed to finish the project on time? There are (15 - 10) = 5 days left.

SECOND PHASE - use individual rate to find # of workers needed

W = (# of workers) * r * t
W = \(\frac{1}{2}\)
# of workers = N = ??
r = \(\frac{1}{80}\)
t = 5 days

W = (#)*r*t
\(\frac{1}{2}= N * \frac{1}{80} * 5\)

\(N =\frac{(\frac{1}{2})}{(\frac{1}{80}*5)}=\frac{(\frac{1}{2})}{(\frac{1}{16})}=\frac{1}{2}*16 = 8\)

(# of workers, N) needed to finish = 8

There are already 4 workers. He needs 4 more.

Answer D

P.S. - I don't use N. I use #, to remind myself what I'm after; "N" isn't as clear. I use N here because formatting goes berserk with the # sign.

The rate for the 4 employees is (1/2)/10 = 1/20.

We see that that the rest of the job has to be completed in 5 days, so the rate must be (1/2)/5 = 1/10.

Since 4 employees have a rate of 1/20, 8 employees would have a rate of 1/10, so 4 more employees must be hired.

Answer: D

Reword the question:

4 employees complete half the project in 10 days. How many additional employees are needed to complete the project in 15 days?

* 4 employees completed half in 10 days
* How do we complete the second half of the project in half the amount of time? We need to double the number of employees.

Therefore, we need another 4 employees. Answer is D.