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a part-time employee whose hourly wage was increased by 25%

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a part-time employee whose hourly wage was increased by 25% [#permalink] New post 25 Feb 2008, 01:37
237. 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?

A.12.5 %
B.20%
C.25%
D.50%
E.75%
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Re: 237. one more each and total amount? really confused! [#permalink] New post 07 Nov 2011, 11:26
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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
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 07:03
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i agree with prasannar.

(1+x)*(1+25%) = 1
(1+x)*5/4 = 1 -> x = 4/5-1 = -1/5 = -20% -> B
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 11:28
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i still cant pick it out ... i didnt have 5 or 4 anywhere, i just have:

1.25x*n = m*x ... and we are looking for (n-m)/n = 1-m/n , and m/n = 1.25 :?
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 17:49
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Thank you Prasannar,

I used your approach and here is mine
original hourly wage: 1$, and total hours worked a week : x
new hourly wage: 1.25, and total hours worked a week: y
1*x = 1.25y
4x=5y
(x-y)/x=1/5 = 20%

Thank you!

@pmenon
pmenon wrote:
i still cant pick it out ... i didnt have 5 or 4 anywhere, i just have:

1.25x*n = m*x ... and we are looking for (n-m)/n = 1-m/n , and m/n = 1.25
i still cant pick it out ... i didnt have 5 or 4 anywhere, i just have:

1.25x*n = m*x ... and we are looking for (n-m)/n = 1-m/n , and m/n = 1.25 :?


You call m: original and n: new. So I think you should set up (n-m)/m, not (n-m)/n.
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 18:26
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sondenso wrote:
237. 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?

A.12.5 %
B.20%
C.25%
D.50%
E.75%


sondesco, in questions like this it helps very much if you draw a quick chart. use 10h for base case and pick a wage per hour that can easily be increased by 25%. (now you can pick anything but by using a "good number" it will be easy to calculate quickly)
let 4 be the base wage per hour, then 25% increase is $5/h. the base income was 10*4=40 , the new income is 10*5=50. but we need it to be 40 so the new hours should be 8, which is a 20 % decrease.
This is a long explanation but just want to show you that if you use a chart, it gets a lot faster.
hope this helps.
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 18:35
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aaaah, yes, you are right !!!!
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 18:36
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pmenon wrote:
Oops, sorry about that prasannar. My mistake :oops:

Can anyone point out where i went wrong in my approach ?


pmenon, nice algebra approach. i like how you use the letters to determine an all case scenario formula. I think the problem here is that you are deleting x on both sides of the equation. no?
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 18:42
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elmagnifico wrote:
sondenso wrote:
237. 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?

A.12.5 %
B.20%
C.25%
D.50%
E.75%


sondesco, in questions like this it helps very much if you draw a quick chart. use 10h for base case and pick a wage per hour that can easily be increased by 25%. (now you can pick anything but by using a "good number" it will be easy to calculate quickly)
let 4 be the base wage per hour, then 25% increase is $5/h. the base income was 10*4=40 , the new income is 10*5=50. but we need it to be 40 so the new hours should be 8, which is a 20 % decrease.
This is a long explanation but just want to show you that if you use a chart, it gets a lot faster.
hope this helps.



Many thanks to "elmagnifico". Clearly your picking number is better! Sorry if I still dont get it, what do you mean "use the chart"?
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Re: 237. one more each and total amount? really confused! [#permalink] New post 26 Feb 2008, 18:49
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OLD - x hrs at $y/hr - total earned: xy
NEW- (x-z) hrs at $1.25/hr - total earned:xy

we have (x-z) (1.25y) = xy
solving for z,
we get 20%.
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 02:02
It is B

take numbers like

First case

100 hours of work say $100

now for the same 100 hours of work $125(25% increase) => 1hour is $1.25 so

100/1.25=80

Thus B
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 04:17
i get c.

original income is given by mx where m is hours worked, and x is original wage. new income is 1.25x*n, where n is new hours worked. we want mx=1.25x*n, and we are looking for (n-m)/n -->1-m/n

m/n=1.25, and so 1-m/n = -0.25 i.e. a 25% decrease.

prasannar, try your approach with an amount other than $1 /hr .... you wont get 20% (try it with $2/hr)
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 06:35
No how would it change? Am I missing some thing?

Let us say the emp. makes $2/hr then for 100 hours he will make $200

now 25% increase $250 for 100 hours

so in order to make $200 per week of 100 hours

reduced # of hours = original weekly income/increased price per hour
=> 200/2.5 =80

it is still B



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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 10:27
Oops, sorry about that prasannar. My mistake :oops:

Can anyone point out where i went wrong in my approach ?
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Re: 237. one more each and total amount? really confused! [#permalink] New post 25 Feb 2008, 11:17
pmenon wrote:
Oops, sorry about that prasannar. My mistake :oops:

Can anyone point out where i went wrong in my approach ?


I think you did 5/4 - 1 instead of 4/5 - 1
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Re: 237. one more each and total amount? really confused! [#permalink] New post 09 Nov 2011, 03:55
Expert's post
sondenso wrote:
237. 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?

A.12.5 %
B.20%
C.25%
D.50%
E.75%


Here is what I like to use in questions where the product of two numbers has to be kept constant:

Weekly income = No of hours * Hourly wage = Constant
If hourly wage increases by 25% i.e. it becomes 5/4 of original value, what should we do to 'no of hours' to keep the Weekly income fixed?
We should multiply 'no of hours' by 4/5 so that the 4 and the 5 cancel each other off and we still have the same weekly income.
When we multiply 'no of hours' by 4/5, it reduces by 1/5 which is 20%. Once you get the hang of it, you can pretty much do it orally.
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Re: 237. one more each and total amount? really confused! [#permalink] New post 09 Nov 2011, 04:26
It is B

let initial revenue=x and time period=t

after increase in revenue 1.25x

Now let "p" the no of hours decreased so now from the above details we can form an equation below

x*t=1.25x*(t-p)

p=20%

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Re: 237. one more each and total amount? really confused!   [#permalink] 09 Nov 2011, 04:26
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