Basic percentage question

[rigby44]

Hi all,

I’m a little embarrassed to have to ask this, but I cannot get my head around the answer.

Why is 3 equal to 60% of 5, but an increase from 3 to 5 is an increase of 66.6667%?

Thank you.

 

[lev888]

Hi all,

I’m a little embarrassed to have to ask this, but I cannot get my head around the answer.

Why is 3 equal to 60% of 5, but an increase from 3 to 5 is an increase of 66.6667%?

Thank you.

A percentage value tells us what proportion quantity A is in relation to quantity B.
So, "3 equal to 60% of 5" states that 3 in relation to 5 is 3/5, or 60%.
But "an increase from 3 to 5 is an increase of 66.6667%" refers to different amounts: 2 in relation to 3 is 2/3, or 66.6667%.

 

[skeeter]

percentage is a comparison

in this case, it is a comparison of the amount of increase relative to the original amount

original amount is 3

the original amount is increased by 2

therefore, the percentage increase from the old to the new amount = (2/3) times 100 = 66.7% rounded

now, we know the new amount is 5
if one were to decrease that amount of 5 by 2, the percentage decrease would be (2/5) times 100 = 40%

this is why one has to be careful when interpreting or calculating percentages

 

[Steven G]

Say you earn $10 per hour and your boss makes an error and gives you a 10% raise. 10% of $10 is $1 so now you are earning $11 per hour. Your boss realizes her mistake (the raise was for another employee) and reduces your pay by 10%. It may sound fair but it is not fair at all. The reason is that 10% of $11 is $1.10. Since $11 - $1.10 = $9.90 you are now making less than $10/hour. How did this happen? Your boss took 10% of different values! 10% of $10 and 10% of $11 are not the same. So 1st you got an increase of $1 and then a decrease of $1.10. Is this clear??