Percent Increase, Decrease explanation

Question

I have a very simple yet somehow confusing question regarding percentage increases/decrease. I am a bit confused about my initial approach for determining percentage difference between two values versus just being just given the easy formula. Without actually knowing the equation by heart this was my initial approach.

If I have an old value A = 350 and a new value of B = 371. What is the percent increase? So I approach this problem in this way

A/B = 0.943397 so it take 4 decimal places. I then take 1-0.943397 = 0.56603 x 100 = 5.6603 percent increase. Therefore (5.6603 * 1/100) * 371 = 21 and this checks out.

But if I use the New Value - Old Value / Old Value I get 6 percent. Where is this error coming from?

Answer 1

You fell in the trap. A relative change can be computed wrt the old value or the new value, you need to be specific about that.

$$\frac{371-350}{350}=\frac{371}{350}-1=6.00\%$$

$$\frac{371-350}{371}=1-\frac{350}{371}=5.66\%$$

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For a similar reason,

$$\begin{align}100+10\%&=110,\\110-10\%&=99\ !?!\end{align}$$

Answer 2

Your second computation is correct (6%).

A “percent increase” compares the change in value (from 350 to 371) to the starting value (350).

Your first computation tells what percent decrease would then have to occur to recover the original value from the increased value. It would be a second change process (from 371 to 350), so its “starting” value would be the increased value (371), so would appear in the denominator.