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# A part-time employee whose hourly wage was increased by 25

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Director
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A part-time employee whose hourly wage was increased by 25 [#permalink]

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22 Oct 2006, 07:25
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A part-time employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 75%
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2014, 08:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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22 Oct 2006, 08:09
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Let original hourly wage be x and let the no of hours worked be y
Total wage will be =x*y
After the increment the wage will be=1.25 x
Now we need to find number of hours worked so that

x*y=1.25x*z i.e z=4/5 y

%decrease = (y-4/5y)/y *100=100/5=20%.

Correct me if I am wrong.
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Re: Number of hours worked [#permalink]

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23 Jul 2011, 21:37
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enigma123 wrote:
A part time employee whose hourly wage was increased by 25% decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

Ans: 20%

Can anyone please tell me the approach to solve this question?

Number of Hours he works today = N
Hourly Wage today = P

Number of Hours he works today = M
Hourly wage after increase = P + 25% = P(1+25/100) = P * (5/4)

To keep the total wage constant :
N*P = M * P * (5/4)

M / N = 4/5
(N-M) / N = 1/5 (fraction by which Number of hours can be decreased while keeping total wage same)

To get the percentage , multiply both side by 100

percent of the number of hours worked be reduced ((N-M) *100/ N) = 100/5 = 20%
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Intern
Joined: 04 May 2011
Posts: 9
Re: Number of hours worked [#permalink]

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23 Jul 2011, 21:58
A = hours of work BEFORE wage increase
B= hours of work AFTER wage increase
when answering about increase or decrease, we need to make the denomenator being the old one.
Here we know that to get the same total wage, A must be 1.25 times of B;
(x is a multiple of #hours, it will get cancel out)

Decrease of hrs = (Bx-Ax)/Ax = (1-1.25)/1.25 = 0.2 = 20%
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Re: Number of hours worked [#permalink]

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04 Aug 2011, 04:28
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Let initial salary be X. Then new salary is 1.25X.
Let the initial no. of hours = h1 and final no. of hours = h2;
given:
X(h1) = 1.25X(h2)
=> h1 = 1.25(h2) (cancelling X on both sides)
We need to find the percent change in no. of hours:

Formula:
Percent change = (New - Original)/Original * 100
=> (h2 - h1)/h1 * 100
Now,
We know that h1 = 1.25(h2)
=> h2/h1 = 1/1.25;
Using dividendo;
we get (h2 - h1)/h1 = (1-1.25)/1.25 ------(1)
We get our answer by multiplying (1) with 100
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Re: Number of hours worked [#permalink]

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04 Aug 2011, 21:38
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enigma123 wrote:
A part time employee whose hourly wage was increased by 25% decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

Ans: 20%

Can anyone please tell me the approach to solve this question?

Consider this:

Total Income = Hourly Wage * No of hours
If we want to keep the total income same,

Hourly Wage * No of hours = New Hourly Wage * New No of hours
Hourly Wage * No of hours = 5/4 * Hourly Wage * New No of hours

So New No of hours/No of hours = 4/5
A decrease of 1/5 i.e. 20%

Or think of it this way:
Since total income has to remain the same, Hourly wage *No of hours has to remain the same. If Hourly wage gets multiplied by 5/4 (an increase of 25%), no of hours should be multiplied by 4/5 to keep their product same i.e. no of hours should be reduced by 1/5 i.e. 20%.

For more on fraction-percentage conversions, check:
http://www.veritasprep.com/blog/2011/02 ... rcentages/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 04 Jun 2011 Posts: 182 Re: Number of hours worked [#permalink] ### Show Tags 04 Aug 2011, 23:23 5 This post received KUDOS 1 This post was BOOKMARKED Although most of the others have provided their explanations using formulae, if you are not comfortable, you can use the below to solve the problem. Its the same as the formulaes depicted below but i guess easier to undestand. let the employee work for$ 100 an hour and a total of 100 hours per month.

His current salary will therefore be 100*100

his salary increases by 25 % --> new salary = 125

since total salary is same
therefore 100*100 = 125 * x

where x is the new hours he needs to work to maintain his monthly inclome

calculating u find x = 80 --> the hours has decreased from 100 to 80 or a 20 % decrease
Director
Joined: 01 Feb 2011
Posts: 703
Re: Number of hours worked [#permalink]

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05 Aug 2011, 07:33
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Hourly Wage

Initial New

$P$125P/100

X hours <X (lets say Y)

given

PX = (125P/100)Y

=> X = (125/100)Y

% decrease = ((x - y)/x )*100

= 20%
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Joined: 27 Feb 2011
Posts: 45
Re: Number of hours worked [#permalink]

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05 Aug 2011, 11:45
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w1 * h1 = w2 * h2

w1 * h1 = 1.25 w1 * h2 => h2 = 4 h1/ 5 = 0.8 h1 => 20% decrease
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Re: Number of hours worked [#permalink]

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05 Aug 2011, 19:47
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hahaha...If you read this question and are a consultant who is paid hourly wages....you will think :

Hey, my current hourly rate is 100 $. Now it has increased by 25%.I can reduce the time I work, because I am now earning more and want to spend time on some of my hobbies/free time :D So how much % time can I work less !!! 100$ per hr(1 hr) = 125$per hr(new time in hrs) ==> new time = 100/125 hrs = 100/25.5 = 20/25 = 80/100 Old time = 1 hr Time decrease = 1-80/100 = 20/100 or 20% I am not putting any approach, just a practical way I would have seen this problem... _________________ Labor cost for typing this post >= Labor cost for pushing the Kudos Button http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html Manager Joined: 05 Oct 2011 Posts: 169 Re: Number of hours worked [#permalink] ### Show Tags 07 Nov 2011, 11:27 1 This post received KUDOS By far the quickest way to solve this problem is by using number plugging as the question is asking a percent in the end. assume: Employee initial salary =$100
Old hours: 20
New salary = \$125
New hours: x

20 * 100 = x * 125
x = 16
Percent of reduction = 4/20 * 100 = 20%

Manager
Joined: 21 Aug 2013
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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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11 Feb 2014, 08:24
Hi,
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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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11 Feb 2014, 08:36
seabhi wrote:
Hi,

______________
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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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23 Sep 2014, 23:40
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Picking works better

100- old wage
50 - old hours
100+25=125 - new wage

50*100=125x
x=40, so 50-40*100/50=20%

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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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30 Sep 2014, 20:57
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Wage ........... No. of Hrs .................. Total

10 ...................... 10 ............................ 100 (Initially)

12.5 .................... 10 .............................. 125 (After increment of 10% wage)

12.5 ...................... x .......................... 100 (Lets say no. of hrs worked = x for 100)

$$x = \frac{100}{12.5} = 8$$

Reduction percentage $$= \frac{10-8}{10} * 100 = 20%$$

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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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26 Aug 2015, 20:32
Hours * Wage per hour = Wage

New Wage -
Hours * 1.25 * Wage per hour = 1.25 * Wage

So, New Wage = 1.25 * Old Wage
Now, forget Hours or Wage per hour. We need to decrease New Wage to make it equal to Old Wage.
So % decrease is
(New Wage - Old Wage)/New Wage = (1.25 - 1)/1.25 = 0.25/1.25 = 1/5 = 20%
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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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21 Sep 2017, 02:23
omg!!
it's really a simple math

reduction in consumption =[( r/100+r)*100]%
=25/125*100
=20%
so, the best answer is 20%
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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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21 Sep 2017, 05:10
Hi Let the number of hours be in 1 week x
and his hourly wage be y
then his total weekly income will be =x*y
His hourly wage increased by 25 % then his new hourly wage will be =1.25y
But he reduces his number of hours worked to maintain same total wage , therefore we have ,
Let a% be the actual decrease in y
Then
1.25axy=xy
a=1/1.25=4/5 =80% so hours are by reduced by 20%
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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]

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25 Sep 2017, 15:37
SimaQ wrote:
A part-time employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 75%

We can let the employee’s wage = w, the number of hours = h, and the percentage reduction = n. Thus:

wh = (1 - n/100)(w)(h)(1.25)

We can divide both sides by wh, convert 1.25 to 5/4, and re-express (1-n/100) as (100 - n)/100 to get:

1 = (100 - n)/100 x 5/4

4/5 = (100 - n)/100

400 = 5(100 - n)

80 = 100 - n

n = 20

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Re: A part-time employee whose hourly wage was increased by 25   [#permalink] 25 Sep 2017, 15:37

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