Percent problem with unknown values from GRE prep book?
March 8th, 2010 | 
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Hello—the question is as follows:
Over the course of a year, a certain factory increased its output by 90%. At the same time, it decreased its total working hours by 20%. By what percent did the factory increase its output per hour?
The answer is 137.5%, not 237.5% like I had gotten as an answer.
Please help if you can!
Posted in gre course
You’re working the problem correctly, just interpreting your result incorrectly. If you let x = the original output of the factory and y = the original number of hours worked, then the new output per hour is
1.9x/.8y = 237.5% (x/y)
But the original output per hour of x/y is the first 100%. So the increase in output per hour is 137.5%.
Let 1000 widgets = the production before increase
So 1000 * 1.9 = 1900 widgets with a 90% improvement
Lets say it took 2080 hours to do 1000 widgets before (this is the actual average working year by the way!)
So they reduced it by:
2080 X .2 = 416 hours
So now, it only takes 2080 – 416 = 1664 hrs/yr to make 1900 Widgets
Before it took, 1000/2080 = 0.48 widget/hr
Now it takes 1900/1664 = 1.142 widget/hr
Net Gain in Productivity: 1.142/0.48 X 100 = 237.9% increase
So you see, your 237.5% figure is correct!
Let me know if you don’t understand ok?
Jim-
You need to take into account that you added 90% to a previous 100% and you subtracted 20% to a previous 100%. So when you figure the new percentage, you have to subtract out the original to find the change in percentage. 237.5-100 is the correct answer.
The definition of percent increase is Amount of Increase/Original Whole * 100
So using your widget example you would want to subtract 0.48 w/hr from 1.142 w/hr to find the amount of increase and divide that by the original whole (0.48). This saves having to subtract out the 100 at the end.
Amt increase/Original whole
(1.142-0.48)/(0.48) = 1.379*100=137.9% (a little off because of rounding earlier)