SOLUTION: Sales reduction force a factory to cut back its output by 20%. By what percent must the reduced sales be increased to allow production to be brought back to normal?

Question 5967: Sales reduction force a factory to cut back its output by 20%. By what percent must the reduced sales be increased to allow production to be brought back to normal?
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
They didn't specify how many units you should start with, right? So let's just say that it could be any number P (that is big enough to be real life enough).

They say that they'll have to cut back production by 20%. That's 20% of what they have now. So far then, we've got where R is the reduced amount of production by 20%.

OK. So then they ask what percent should R be increased by to get back to that original P, right? No, it's not 20%, since 20% of the reduced price is less than the 20% used to reduce P to R before. In other words, increasing the reduced by 20% won't get you back to where you were.
So is the equation we'll use. We'll have to solve for c to get that percentage increase. First up, we'll have to do a substitution. Substitute P - 0.20P for R:

<--- Subtract P from both sides.

<--- Add 0.20P to both sides

<---- Divide both sides by (P-0.20P) to solve for c

<---- Factor out the P in the denominator

<----- The P's cancel. This says that it doesn't matter how many units you'll start with.

<----- Finally, c = 25%. AKA, if you reduce anything by 20% of its size, you'll have to increase the shrunken size by 25% to get back to the original size.
RELATED QUESTIONS
Over the course of a year, a certain factory increased its output by 90%. At the same... (answered by ankor@dixie-net.com)

Because of a decrease in available manpower, a toy factory reduced its monthly output by... (answered by Alan3354)

I would appreciate some help on this question please! During a sale, the price of a... (answered by josmiceli)

The price of a color printer is reduced by 30% of its original price. When it still does... (answered by josmiceli)

A WORKERS SALARY WAS REDUCED BY 60%. BY WHAT PERCENT MUST THE NEW SALARY BE RAISED TO... (answered by solver91311)

The price of an item that sold for $240 was reduced by 33 1/3%. By what percent must the... (answered by josmiceli)

A dress is marked down by 20% in an effort to boost sales for one week. After that week, (answered by josmiceli)

In 2008, Home Depot�s sales amounted to $71,300,000,000. In 2009, its sales were... (answered by Ryan O'Hara)

The original price of an smartphone was increased by 25%. A sale brought the price of... (answered by josgarithmetic,ikleyn)