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# A part-time employee whose hourly wage was decreased by 20 percent dec

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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10 Feb 2015, 08:36
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15% (low)

Question Stats:

83% (01:20) correct 17% (01:10) wrong based on 65 sessions

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A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased?

A. 12.5%
B. 20%
C. 25%
D. 50%
E. 100%

Kudos for a correct solution.

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Re: A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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10 Feb 2015, 11:49
1
Plugging in some easy numbers

Assume
Hours Worked: 10 hours
Hourly Wage: 10 $Weekly Wage: 100$

After decrease of 20 % in Hourly Wage would become 8 $Hours Worked would have to be 12.5 hours in order to maintain Weekly Wage of 100$

% increase in number of hours worked = (12.5 - 10 ) / 10
= 0.25 * 100
= 25%

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Re: A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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10 Feb 2015, 13:12
1
Quote:
A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased?

A. 12.5%
B. 20%
C. 25%
D. 50%
E. 100%

At first we got 1=100%
Decrease by 20 % -> 5/5 --> 4/5
The number of hours worked --> take the reciprocal of the decreased value. -> 5/4 -> 125% so its 25%
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Re: A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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10 Feb 2015, 20:29
2

Per Hr Wage ................. No. of Hours ................. Total

100 .................................... 1 ............................. 100 (Assumption)

80 ....................................... $$\frac{100}{80}$$ .................... 100 (Per hour wage decreased by 20%; total amount remains constant)

No. of hours increase % $$= (\frac{100}{80} - 1)*100 = \frac{20}{80} * 100 = 25%$$
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Re: A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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11 Feb 2015, 04:41
1
eddyki wrote:
Quote:
A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased?

A. 12.5%
B. 20%
C. 25%
D. 50%
E. 100%

At first we got 1=100%
Decrease by 20 % -> 5/5 --> 4/5
The number of hours worked --> take the reciprocal of the decreased value. -> 5/4 -> 125% so its 25%

Here is the reason you take reciprocal:

Total old wage = Total new wage
HWage * Hours = HWage*(4/5) * NewHours
NewHours = (5/4) * Hours

This is an increase of 1/4 i.e. 25%.
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Re: A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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11 Feb 2015, 07:03
1
Came to finally with option C
hours wage total
10hrs 100 10*100= 1000
xhrs 20% reduced from initial so now 80 x*80=1000

x=12.hrs
2.5hrs extra which is 25% extra hours put in.

kudos for me too....
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Joined: 02 Sep 2009
Posts: 58396
Re: A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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16 Feb 2015, 05:41
Bunuel wrote:
A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased?

A. 12.5%
B. 20%
C. 25%
D. 50%
E. 100%

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked will be 25% greater than the original number. The answer is C.
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Re: A part-time employee whose hourly wage was decreased by 20 percent dec  [#permalink]

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13 Apr 2019, 10:04
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Re: A part-time employee whose hourly wage was decreased by 20 percent dec   [#permalink] 13 Apr 2019, 10:04
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