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

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Director
Joined: 06 Feb 2006
Posts: 882
A part-time employee whose hourly wage was increased by 25 [#permalink]

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Updated on: 11 Feb 2014, 09:34
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Question Stats:

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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%

Originally posted by SimaQ on 22 Oct 2006, 08:25.
Last edited by Bunuel on 11 Feb 2014, 09:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Joined: 01 Oct 2006
Posts: 486

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22 Oct 2006, 09:09
1
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%.
Thus my answer is B.

Correct me if I am wrong.
Manager
Joined: 28 May 2011
Posts: 172
Location: United States
Concentration: General Management, International Business
GMAT 1: 720 Q49 V38
GPA: 3.6
WE: Project Management (Computer Software)
Re: Number of hours worked [#permalink]

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23 Jul 2011, 22:37
1
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, 22:58
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%
Manager
Joined: 25 Sep 2010
Posts: 66
Schools: HBS, LBS, Wharton, Kelloggs, Booth
Re: Number of hours worked [#permalink]

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04 Aug 2011, 05:28
1
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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8101
Location: Pune, India
Re: Number of hours worked [#permalink]

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04 Aug 2011, 22:38
4
2
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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Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 04 Jun 2011 Posts: 174 Re: Number of hours worked [#permalink] ### Show Tags 05 Aug 2011, 00:23 5 1 Although most of the others have provided their explanations using formulae, if you are not comfortable, you can use the below to solve the problem. Its the same as the formulaes depicted below but i guess easier to undestand. let the employee work for$ 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: 686
Re: Number of hours worked [#permalink]

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05 Aug 2011, 08:33
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%
Intern
Joined: 27 Feb 2011
Posts: 43
Re: Number of hours worked [#permalink]

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05 Aug 2011, 12:45
w1 * h1 = w2 * h2

w1 * h1 = 1.25 w1 * h2 => h2 = 4 h1/ 5 = 0.8 h1 => 20% decrease
Manager
Status: On...
Joined: 16 Jan 2011
Posts: 171
Re: Number of hours worked [#permalink]

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05 Aug 2011, 20:47
hahaha...If you read this question and are a consultant who is paid hourly wages....you will think :

Old hours: 20
New salary = $125 New hours: x 20 * 100 = x * 125 x = 16 Percent of reduction = 4/20 * 100 = 20% Answer: B Manager Joined: 22 Aug 2013 Posts: 88 Schools: ISB '15 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 11 Feb 2014, 09:24 Hi, Please add OA. Thanks _________________ Veritas Prep - 650 MGMAT 1 590 MGMAT 2 640 (V48/Q31) Please help the community by giving Kudos. Math Expert Joined: 02 Sep 2009 Posts: 46194 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 11 Feb 2014, 09:36 seabhi wrote: Hi, Please add OA. Thanks ______________ Done. Added the OA. _________________ Director Joined: 23 Jan 2013 Posts: 597 Schools: Cambridge'16 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 24 Sep 2014, 00:40 1 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% B SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1837 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 30 Sep 2014, 21:57 2 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 $$= \frac{10-8}{10} * 100 = 20%$$ Answer = B _________________ Kindly press "+1 Kudos" to appreciate Manager Joined: 11 Oct 2013 Posts: 115 Concentration: Marketing, General Management GMAT 1: 600 Q41 V31 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 26 Aug 2015, 21:32 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% _________________ Its not over.. Intern Joined: 18 Sep 2017 Posts: 5 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 21 Sep 2017, 03:23 omg!! it's really a simple math just follow the rule....... reduction in consumption =[( r/100+r)*100]% =25/125*100 =20% so, the best answer is 20% hope it is helpful!!! VP Status: Learning Joined: 20 Dec 2015 Posts: 1157 Location: India Concentration: Operations, Marketing GMAT 1: 670 Q48 V36 GRE 1: 314 Q157 V157 GPA: 3.4 WE: Manufacturing and Production (Manufacturing) Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 21 Sep 2017, 06:10 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% _________________ Please give kudos if you found my answers useful Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2738 Location: United States (CA) Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 25 Sep 2017, 16:37 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 Answer: B _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions SC Moderator Joined: 22 May 2016 Posts: 1755 A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 27 Sep 2017, 15:02 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% 30-sec approach: By what percent must hours worked decrease so that total weekly income remains unchanged? By 1 - (fractional inverse of the percent increase) When the original quantity is the start and end value, percent increase and percent decrease are inversely proportional. Use a fraction for the percent increase of one factor. Flip that fraction. Subtract from 1. The result is the percent by which the other factor must decrease. Thus: $$xy = 1$$ $$x$$ increases by 25% = 1.25* = $$\frac{5}{4}$$ Flip to $$\frac{4}{5}$$ and subtract from 1 to yield percent by which $$y$$ must decrease: $$1 - \frac{4}{5} = \frac{1}{5}$$ = 20 percent (Or assess the flipped fraction: $$\frac{4}{5}$$ = .8 = 80 percent = 20 percent decrease) Note: if $$xy = 1$$, then $$\frac{5}{4}x * \frac{4}{5}y = 1$$ Longer method, w/ numbers (no need!): x = wage per hour =$20
y = # of hours worked = 10

(Wage per hour)(# of hours) = total weekly income

Total wages = $20 * 10 =$200

x, $20, increases by 25 percent: x = $$\frac{5}{4}(20)$$ = 25. We want$200. What is y?

$$(25)(y)= 200$$, so $$y = 8$$

By what percent did y decrease?

$$\frac{new-old}{old} =\frac{10-8}{10} =\frac{1}{5} = .20 * 100 =$$ 20%

In other words, when you want the original quantity to remain the same and one factor increases by a percent, to calculate the corresponding percent decrease, finding and flipping the fraction works.

*An increase of 25 percent =
$$1.25 =1\frac{25}{100} = 1\frac{1}{4} = \frac{5}{4}$$
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A part-time employee whose hourly wage was increased by 25   [#permalink] 27 Sep 2017, 15:02
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# A part-time employee whose hourly wage was increased by 25

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