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Decrease hours to keep income the same

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by kobel51 » Tue Mar 18, 2014 8:53 am
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%
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by Patrick_GMATFix » Tue Mar 18, 2014 9:08 am
We can plug in to solve quickly. Suppose we start with wage=$4 and hours=5, making income $20. If wage increase by 25% to $5, hours will drop to 4, a 20% drop.

The answer is B. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by Bill@VeritasPrep » Tue Mar 18, 2014 9:41 am
Patrick_GMATFix wrote:We can plug in to solve quickly. Suppose we start with wage=$4 and hours=5, making income $20. If wage increase by 25% to $5, hours will drop to 4, a 20% drop.
That's how I'd do it. Percent changes with no actual values? Plug in and go!
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by Abhishek009 » Tue Mar 18, 2014 10:03 am
kobel51 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%

Earlier -

Let hours worked be 10

Hourly wage was 10

Earning = 100


After the increase -

Hourly Wage is 12.50

Earnings = 100

So , Total hours worked now is 100/12.50 =>8 hours.


Decrease in hours worked is ( 2/10 ) *100 % => 20%
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by ceilidh.erickson » Tue Mar 18, 2014 1:35 pm
Plugging in values is certainly the easiest approach in a case like this, where you have percents but no actual values. If you're interested in what the algebraic approach would look like, though, here it is:

original wage, hours, and income:
w*h = I

increased wage, decreased hours (represented by "x"), and income:
(1.25w)(xh) = I

Substitute wh for I:
(1.25w)(xh) = wh

Divide both sides by wh:
1.25x = 1
x = 0.8

80% of the hours = 20% reduction in hours.
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