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# A grocery store stocker whose hourly wage was increased by 50 percent

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Posts: 43361
A grocery store stocker whose hourly wage was increased by 50 percent [#permalink]

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27 Dec 2017, 00:06
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A grocery store stocker whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that his total weekly income would remain unchanged. By approximately what percent should the number of hours worked be reduced?

A. 12.5%
B. 20%
C. 25%
D. 33.33%
E. 66.67%
[Reveal] Spoiler: OA

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Re: A grocery store stocker whose hourly wage was increased by 50 percent [#permalink]

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27 Dec 2017, 00:35
Bunuel wrote:
A grocery store stocker whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that his total weekly income would remain unchanged. By approximately what percent should the number of hours worked be reduced?

A. 12.5%
B. 20%
C. 25%
D. 33.33%
E. 66.67%

We'll solve this with a straightforward calculation.
This is a Precise approach.

The stocker's salary increased from 100% to 150% after the raise.
To lower it back to 100% he must decrease his new salary by 50% out of 150%.
50%/150% = 1/3 so he must reduce his hours by 1/3.
(D) is our answer.
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Re: A grocery store stocker whose hourly wage was increased by 50 percent [#permalink]

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28 Dec 2017, 02:49
Bunuel wrote:
A grocery store stocker whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that his total weekly income would remain unchanged. By approximately what percent should the number of hours worked be reduced?

A. 12.5%
B. 20%
C. 25%
D. 33.33%
E. 66.67%

$$Wage*Hours=Income$$

Before the increase his wage was $10 and he worked 9hrs, so $$10*9=90$$ After the increase his wage went to$15 and his income stayed the same, so $$15*hrs=90$$, $$hrs=90/15=6$$

Percent Change: $$1-\frac{After}{Before}=1-\frac{6}{9}=3/9=1/3=33.33$$%

(D) is the answer.
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Re: A grocery store stocker whose hourly wage was increased by 50 percent [#permalink]

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28 Dec 2017, 08:57
Bunuel wrote:
A grocery store stocker whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that his total weekly income would remain unchanged. By approximately what percent should the number of hours worked be reduced?

A. 12.5%
B. 20%
C. 25%
D. 33.33%
E. 66.67%
Attachment:

Hourly Wage.PNG [ 2.71 KiB | Viewed 181 times ]
$$\frac{100}{15} = 6.67$$

Thus, percentage reduction in hours required is 33.33%, answer will be (E)

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A grocery store stocker whose hourly wage was increased by 50 percent [#permalink]

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28 Dec 2017, 16:16
Abhishek009 wrote:
Bunuel wrote:
A grocery store stocker whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that his total weekly income would remain unchanged. By approximately what percent should the number of hours worked be reduced?

A. 12.5%
B. 20%
C. 25%
D. 33.33%
E. 66.67%
Attachment:
Hourly Wage.PNG
$$\frac{100}{15} = 6.67$$

Thus, percentage reduction in hours required is 33.33%, answer will be (E)

Hi Abishek, I think you mean the answer is (D) 33.33%

The numbers of hours worked reduced from 10 to 6.67 = 33.33% reduction, (D).

Last edited by exc4libur on 29 Dec 2017, 02:10, edited 1 time in total.
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A grocery store stocker whose hourly wage was increased by 50 percent [#permalink]

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28 Dec 2017, 18:07
Bunuel wrote:
A grocery store stocker whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that his total weekly income would remain unchanged. By approximately what percent should the number of hours worked be reduced?

A. 12.5%
B. 20%
C. 25%
D. 33.33%
E. 66.67%

Percent increase and percent decrease are inversely proportional when the original value is constant (or when returning to the original is the goal).

When there is a percent increase and decrease problem and the original is constant or sought after:

1) Find the fraction for the percent increase or decrease;

2) Flip the fraction;

3) If a percent increase is needed as offset, subtract the flipped fraction FROM 1. Change the decimal to a percent. Done. OR

4) If a percent decrease is needed as offset, subtract 1 from the flipped fraction. Change the decimal to a percent. Done.

Here, we have a 50 percent increase in weekly wage.

The worker wants to maintain the same weekly pay.

By what percent must he reduce his number of hours worked?

1) Fraction: A 50 percent increase = $$1.5 = 1 \frac{1}{2} = \frac{3}{2}$$

2) Flip that fraction: $$\frac{3}{2} --> \frac{2}{3}$$

3 ) Subtract from 1: $$(1 - \frac{2}{3}) = \frac{1}{3} = .3333 \approx{33.33}$$ % is the percent by which he must decrease his hours to maintain his original weekly pay.

To offset a percent increase: (1 - fractional inverse of the increase)
To offset a percent decrease: (fractional inverse of the decrease - 1)
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A grocery store stocker whose hourly wage was increased by 50 percent   [#permalink] 28 Dec 2017, 18:07
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# A grocery store stocker whose hourly wage was increased by 50 percent

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