A part-time employee whose hourly wage was increased by 25 : GMAT Problem Solving (PS)
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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.
Senior Manager
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22 Oct 2006, 08:09
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.
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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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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
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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Expert's post
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 $199 Veritas Prep Reviews Manager Joined: 04 Jun 2011 Posts: 189 Followers: 0 Kudos [?]: 52 [5] , given: 21 Re: Number of hours worked [#permalink] ### Show Tags 04 Aug 2011, 23:23 5 This post received KUDOS 1 This post was BOOKMARKED Although most of the others have provided their explanations using formulae, if you are not comfortable, you can use the below to solve the problem. Its the same as the formulaes depicted below but i guess easier to undestand. let the employee work for$ 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
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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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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 :

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: 21 Aug 2013 Posts: 113 Schools: ISB '15 Followers: 2 Kudos [?]: 29 [0], given: 60 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 11 Feb 2014, 08:24 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: 36583 Followers: 7087 Kudos [?]: 93288 [0], given: 10555 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 11 Feb 2014, 08:36 seabhi wrote: Hi, Please add OA. Thanks ______________ Done. Added the OA. _________________ Director Joined: 23 Jan 2013 Posts: 579 Schools: Cambridge'16 Followers: 1 Kudos [?]: 42 [1] , given: 40 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 23 Sep 2014, 23:40 1 This post received KUDOS 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: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 1935 [2] , given: 193 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 30 Sep 2014, 20:57 2 This post received KUDOS 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 Current Student Joined: 11 Oct 2013 Posts: 124 Concentration: Marketing, General Management GMAT 1: 600 Q41 V31 Followers: 1 Kudos [?]: 51 [0], given: 137 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 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% _________________ Its not over.. GMAT Club Legend Joined: 09 Sep 2013 Posts: 13468 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] ### Show Tags 06 Sep 2016, 11:52 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 06 Sep 2016, 11:52 Similar topics Replies Last post Similar Topics: 3 A part-time employee’s hourly wage was increased by 10%. She decided 2 07 Mar 2016, 08:19 5 A part-time employee whose hourly wage was decreased by 20 percent dec 6 10 Feb 2015, 07:36 2 Ian is paid an hourly wage, totaling$400 for h hours of work in a wee 8 21 Jan 2015, 01:23
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# A part-time employee whose hourly wage was increased by 25

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