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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Percentage reduction problem - Help wanted please ##### This topic has 1 expert reply and 2 member replies ## Percentage reduction problem - Help wanted please 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 Legendary Member Joined 20 Jun 2007 Posted: 1153 messages Followed by: 2 members Upvotes: 146 Target GMAT Score: V50 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. Legendary Member Joined 28 Aug 2008 Posted: 2467 messages Followed by: 11 members Upvotes: 331 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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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 employeeâ€™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

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