Problem Solving

The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was raised by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?

Apparently the answere is 24%, can someone tell me the most efficient way to arrive at that conclusion? I just can't get it. It might be dumb I know, but any bone thrown my way would be much appreciated.

Let the output of a factory is 100

First,increased by 10 %=110

due to holiday rush,it increase by 20%=110+22=132

Net increase=(100/132)*100=75.9~=76%

Increment=100-76=24%

Hope it clears.......

I agree, that's a great way to solve it. This is a very common question type - where you're asked for a percent or fraction of some unknown. To make these problems easier, just make up a number for the unknown.

the answer cant be 24 and if it is so then i have nothing to say.

Let output before increase = 100
after 10% increase, output will be = 100+10 = 110
after next 20% increase, the increase will be = 110 * 20/100 = 22
total output = 110+22 = 132
total increase = 32
percentage increase = 32/100 * 100 = 32%

it cant be 24% anyway.

hope you understand

Whoops, looks like I didn't read the previous post well enough! I agree that it's not 24.

100 increases to 110
110 increases to 132

100 to 132 is a 32% increase.

I agree with stubbornp that it is 24%. It's asking for the % decrease to get it back to the originial, not the % increase that has occurred. 132 decreased by 24% would give you ~100.

Let intial amount =100$
For Subsequent % change formula, let x% and y% increase , then formula .... x+y+(xy/100)...this is total change in %.
In above example , 10% & then 20% increase,putting this in formula =
10+20+(10*20 /100) = 32%.So total change in amount =32 $
New amount =132$,


So, If we have to get back to original, % decrease = 132-100 = 32 => (32*100)/132 = 24.24 %
So, ans should be 24% OA pls.

Okay, don't listen to me. Apparently I DID read it correctly the first time. Yes, it's asking for the % decrease back to the original, which would be 32/132 = 24%.