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Percentage reduction problem - Help wanted please

This topic has 1 expert reply and 2 member replies

Percentage reduction problem - Help wanted please

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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%

The answer is B

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madsport 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%

The answer is B
Wage increased 25%
Weekly income remains the same

let initial wage = $10/hour
hours worked during the week = 5

10*5 = $50 [ weekly income]

wage increased 25%
10*1.25 = 12.5

Weekly income remains unchanged
12.5x =50
x=4

percentage change

5-4/5 *100 = 20%

Hence B is the answer.

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For percentage problems pick 100 (works most of the times) and pick other numbers if you have to the ones that are divisible by 100, easy to multiply etc...

Let us assume that the employee works 10 hours a week
Let the hourly hourly wage be 100.
New hourly wage = 125

Original salary = 100*10 = 1000
New Salary = 125*10 = 1250

To get 1250 he has to work 10 hours.
To get 1000(original salary) = ?? hours

salary hours
1250 10
1000 ?

10/1250*1000 = 8

Therefore the difference in hours = 2 It doesnt stop here since we need to find 2 is what % of10.

100/10*2 = 20%

Therefore there needs to be a 20% reduction of hours with the hourly wage increase so that he earns the same as before($1000)

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madsport 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%
We can let the employee’s wage = w, the number of hours = h, and the percentage reduction = n. Thus:

wh = (1 - n/100)(w)(h)(1.25)

We can divide both sides by wh, convert 1.25 to 5/4, and re-express (1-n/100) as (100 - n)/100 to get:

1 = (100 - n)/100 x 5/4

4/5 = (100 - n)/100

400 = 5(100 - n)

80 = 100 - n

n = 20

Answer: B

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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