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

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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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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]
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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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]
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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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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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... Manager Joined: 05 Oct 2011 Posts: 125 Own Kudos [?]: 91 [5] Given Kudos: 62 Re: Number of hours worked [#permalink] 2 Kudos 3 Bookmarks 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% Answer: B Senior Manager Joined: 23 Jan 2013 Posts: 424 Own Kudos [?]: 268 [3] Given Kudos: 43 Schools: Cambridge'16 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 1 Kudos 2 Bookmarks 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 Joined: 27 Dec 2012 Status:The Best Or Nothing Posts: 1558 Own Kudos [?]: 7292 [3] Given Kudos: 193 Location: India Concentration: General Management, Technology WE:Information Technology (Computer Software) Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 2 Kudos 1 Bookmarks 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 Manager Joined: 11 Oct 2013 Posts: 70 Own Kudos [?]: 288 [0] Given Kudos: 137 Concentration: Marketing, General Management GMAT 1: 600 Q41 V31 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 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% Intern Joined: 18 Sep 2017 Posts: 4 Own Kudos [?]: 4 [3] Given Kudos: 3 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 2 Kudos 1 Bookmarks 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!!! Director Joined: 20 Dec 2015 Status:Learning Posts: 864 Own Kudos [?]: 570 [0] Given Kudos: 755 Location: India Concentration: Operations, Marketing GMAT 1: 670 Q48 V36 GRE 1: Q157 V157 GPA: 3.4 WE:Engineering (Manufacturing) Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 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% Target Test Prep Representative Joined: 14 Oct 2015 Status:Founder & CEO Affiliations: Target Test Prep Posts: 19133 Own Kudos [?]: 22641 [1] Given Kudos: 286 Location: United States (CA) Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 1 Bookmarks Expert Reply 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 Senior SC Moderator Joined: 22 May 2016 Posts: 5327 Own Kudos [?]: 35758 [2] Given Kudos: 9464 A part-time employee whose hourly wage was increased by 25 [#permalink] 1 Kudos 1 Bookmarks Expert Reply 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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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]
Can someone explain why my method is wrong...I'm getting nowhere close to the correct answer:

xy = 5x/4 * [(100-y)/100] .. so solve for y here.
xy = (500x-5xy)/400
400xy = 500x-5xy
405xy = 500x
y = 500/405 = 10/9 ... but obviously this is not the answer and I can't see what mistake I made.

If I use 100 = xy to start...then I can get the answer because 5x/4 just becomes 125 but if I try to just use variables throughout the equation, I mess it up so badly. Any help please!!
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Re: A part-time employee whose hourly wage was increased by 25 [#permalink]
yogeshsheth wrote:
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%.