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

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Manager
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A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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25 Nov 2017, 14:52
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A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1
B) 2
C) 3
D) 4
E) 5
[Reveal] Spoiler: OA

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Re: A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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25 Nov 2017, 15:21
Hadrienlbb wrote:
A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1
B) 2
C) 3
D) 4
E) 5

Let the total work be 60 emp-days and the rate of each employee be 1 emp-days/day.
After 10 days, only half of the work is completed. Therefore, remaining work= (1/2)*60 emp-days= 30 emp-days.
To complete the remaining work in 5 days, we need (30 emp-days/5 days) = 6 employees.
Hence, the manager needs to hire 2 additional employees to complete the work in the stipulated time.

Answer should be B.

Hope this helps.

Cheers.
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Re: A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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25 Nov 2017, 16:06
Madnov2017 wrote:
Hadrienlbb wrote:
A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1
B) 2
C) 3
D) 4
E) 5

Let the total work be 60 emp-days and the rate of each employee be 1 emp-days/day.
After 10 days, only half of the work is completed. Therefore, remaining work= (1/2)*60 emp-days= 30 emp-days.
To complete the remaining work in 5 days, we need (30 emp-days/5 days) = 6 employees.
Hence, the manager needs to hire 2 additional employees to complete the work in the stipulated time.

Answer should be B.

Hope this helps.

Cheers.

You are taking a wrong assumption. The manager hired 4 employees to complete a work in 15 days. This doesn't necessarily mean that the work is of (15*4) units.

Using your approach, in 10 days 4 employees can complete 40 units of work. Therefore, remaining would be 40 units, since in 10 days only half the work was completed.
40 units can be completed in 5 days by (40/5) = 8 employeess.

Therefore, additional 8-4=4 employees must be included. Hence, answer is D.

Cheers,
Kabir

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A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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25 Nov 2017, 16:40
Hadrienlbb wrote:
A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1
B) 2
C) 3
D) 4
E) 5

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

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Re: A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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25 Nov 2017, 22:26
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

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Re: A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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26 Nov 2017, 00:20
Hadrienlbb wrote:
A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1
B) 2
C) 3
D) 4
E) 5

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
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A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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26 Nov 2017, 17:58
Hadrienlbb wrote:
A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1
B) 2
C) 3
D) 4
E) 5

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.

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Re: A manager hired 4 employees to complete a certain project in 15 days. [#permalink]

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29 Nov 2017, 09:58
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Hadrienlbb wrote:
A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

A) 1
B) 2
C) 3
D) 4
E) 5

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
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Re: A manager hired 4 employees to complete a certain project in 15 days.   [#permalink] 29 Nov 2017, 09:58
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