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Ian is paid an hourly wage, totaling $400 for h hours of work in a wee

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Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 21 Jan 2015, 02:23
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Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?

A. $200
B. $375
C. $400
D. $425
E. $600

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 21 Jan 2015, 07:30
B... ans 400*1.25*.75
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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 21 Jan 2015, 11:20
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let No of hours ian worked = h
and wage per hour = w

there fore w*h = 400

if he decides to work 25% fewer hours = 0.75 * h
and 25% more age is paid = 1.25 * w

therefore 1.25*w*0.75*h = 1.25*0.75*400 = 375

ans - B

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 21 Jan 2015, 11:40
Let the hourly wage be W

So, W * h = 400
or, W= 400 / h -------------- first equation

Now applying the given increase/decrease conditions on the variables.

Hourly wage increased by 25% . So from first equation

W = 400/h + 25 * 400 /100h = 500/h -----second equation

No of working hours decreased by 25%

h = h - h*25/100 = 3h/4 ------------ third equation

Total wage for the week according to new conditions = 500 * 3h / 4h ------multiplying second and third equation

= $375

Ans B

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 21 Jan 2015, 12:23
Let Pay/hr = p..

hp = 400...

Now 0.75h*1.25p = 0.75*1.25*hp = 0.75*1.25*400 = 375 = B

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 21 Jan 2015, 14:57
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Hi All,

Questions such as this one can be approached in a variety of different ways - you can TEST VALUES, do the "math" in lots of different ways, and even use some pattern-matching along with the answer choices to quickly get to the correct answer....

We're told that Ian is paid $400 for H hours of work. So we can create the following equation....

400 = (H)(P)

H = # of hours worked
P = pay/hour

We're asked what Ian's pay would be if his pay increases by 25% and his hours decrease by 25%. This info can be written as decimals or fractions....Here's how the "new" equation will look....

25% increase = 5/4
25% decrease = 3/4

(5/4)P(3/4)(H)

(5/4)(3/4)HP = (15/16)(HP)

15/16HP is a little less than 1HP (= $400), so we're looking for an answer that's a little less than $400. There's only one answer that's close...

Final Answer:
[Reveal] Spoiler:
B


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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 21 Jan 2015, 22:53
Bunuel wrote:
Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?

A. $200
B. $375
C. $400
D. $425
E. $600

Kudos for a correct solution.


Total wager = h hours * wages per hour (w).
h*w = 400.
In given condition we are asked (1.25w)*(0.75) = 1.25*0.75*400 = 375 dollars.

Answer B.

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 22 Jan 2015, 00:52
Answer = B. $375

Number of Hours.................... Per hour cost .................... Total

h ................................................. \(\frac{400}{h}\) ......................... 400

\(h * \frac{75}{100}\) .................................. \(\frac{400}{h} * \frac{125}{100}\) ............... (Hours decreased by 25%; wage increased by 25%)

\(Total = h * \frac{75}{100} * \frac{400}{h} * \frac{125}{100} = 375\)
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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 20 Jun 2017, 19:11
Hourly wage \(= \frac{400}{h}\)

Increase in hourly wage is\(\frac{5}{4} *\frac{400}{h} = \frac{500}{h}\)

Decrease in hours worked is\(\frac{3h}{4} * \frac{500}{h} = 375\)

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee [#permalink]

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New post 22 Sep 2017, 14:21
Bunuel : please provide OA after review. The answer is Option B.

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Re: Ian is paid an hourly wage, totaling $400 for h hours of work in a wee   [#permalink] 22 Sep 2017, 14:21
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