# Problem regarding percentage increases.

#### Strikera

##### New member
Ran into a problem which is driving me nuts and would appreciate any assistance on the problem.

Problem:

A factory increases it's production by 10%. The factory then increases it's production by another 20%. To return to the original production (before the 10 and 20% increases) how much production would the factory need to reduce?

The answer is 24% but I have no idea on how they arrived at that number or the steps needed to properly approach the problem.

Thanks in advance for any help!

#### skeeter

##### Senior Member
let P = production level

increase P by 10% = (1.10)P

increase the new level by another 20% = (1.20)(1.10)P = (1.32)P

to reduce back to P ... P = (1/1.32)(1.32)P

1/1.32 = approx 0.76 of the last level of production ... a 24% decrease.

#### Denis

##### Senior Member
Striker, when you have "no idea", make up a simple example,
like let initial production = 1000:
1000 + 10% = 1000 + 100 = 1100
1100 + 20% = 1100 + 220 = 1320

Now you can "see" that 1320 needs to be reduced back to 1000,
so a reduction of 320: kapish?

#### pka

##### Elite Member
Here is a sure-fire method to do all these problems:
$$\displaystyle \frac{{New - Old}}{{Old}}$$

This works for % of increase or decrease.

#### tkhunny

##### Moderator
Staff member
...unless, of course, Old = 0.

#### stapel

##### Super Moderator
Staff member
tkhunny said:
...unless, of course, Old = 0.
But if you're starting from zero, then "percent change" has no meaning, so it's a moot point, isn't it...?

Eliz.

#### tkhunny

##### Moderator
Staff member
It absolutely is not moot if your employer INSISTS on a "Percent Change" in that important report he's about to present to the Board of Directors.

It can be a difficult argument to convince said employer that the question is pointless.

Try this in your next boardroom...

Results by quarter

1) -5 a loss
2) -4 less loss
3) -3 less loss
4) -2 less loss
5) -1 less loss
6) 0 less loss
7) 5 big gain

Percent change by quarter

2) +20%
3) +25%
4) +33%
5) +50%
6) +100%
7) Pointless Data.

They WILL find it unsatisfactory.

It is good to be aware of this problem. That's all I'm saying. If your data can reach zero, your audience should be warned well before the event.