Thread: Simple Percentage Logic

Found this one confused a lot of people for the most obvious reasons.
Anyways, here it is:

"Bill sells suits for a living. He buys a suit and puts it on sale for 133 and 1/3 percent of it's wholesale price. Harry purchases this suit, only to find that it is too small. Harry then sells it back to Bill for the wholesale price. What is the percentage loss incurred by Harry?"
Post your solutions
Edit: note, percentage loss refers to the amount harry lost by selling it back for a lower price

w = wholesale, s = selling
w(1 + 4/3) = s

s(1 + x) = w
1 + x = w/s
x = w/s - 1

Example:
120(1 + 4/3) = 280

x = 120/280 - 1 = -.57142... : so loss of ~57%

incorrect

Harry bought it for say 133+1/3 dollars and sold it for 100 dollars. (1/3 dollar isn't an actual amount, but all we care about is the ratio.)

100 is 3/4 of 133+1/3. So he incurred a 25% loss.

Well, ain't spending time looking for a play on words;

.57142... * 280 = 160, which is what he lost: 280 - 120 = 160

would 's' not be equal to 1 + 1/3 ?
(Undefined is correct)

Originally Posted by 99.95

would 's' not be equal to 1 + 1/3 ?
(Undefined is correct)

NO.
A 10% increase on $100 results in 100(1 + .10) = 110
Similarly, a (133.333...)% increase results in 100(1 + 1.33333) = 233.33

Originally Posted by Wilmer

NO.
A 10% increase on $100 results in 100(1 + .10) = 110
Similarly, a (133.333...)% increase results in 100(1 + 1.33333) = 233.33

I don't think there is any play on words or ambiguity here; the problem states "puts it on sale for 133 and 1/3 percent of it's wholesale price". This is different from a 133+1/3 percent increase.

Originally Posted by undefined

I don't think there is any play on words or ambiguity here; the problem states "puts it on sale for 133 and 1/3 percent of it's wholesale price". This is different from a 133+1/3 percent increase.

Before I resign or commit suicide, can you tell me WHY?

Originally Posted by Wilmer

Before I resign or commit suicide, can you tell me WHY?

Umm.. I'm not sure what's going on emotionally or if there's some joke I'm missing but..

Suppose wholesale price is $3.

133+1/3 percent of $3 is $4.

So if you sell at 133+1/3 percent of wholesale price, the sale price is $4.

If you increase by 133+1/3 percent, you increase by $4, and the sale price is $7.

Am I missing something?

Originally Posted by undefined

Umm.. I'm not sure what's going on emotionally or if there's some joke I'm missing but..
Am I missing something?

Just a joke, n/0; I'm the one that missed something; I read this:
"He buys a suit and puts it on sale for 133 and 1/3 percent of it's wholesale price."
as a profit margin of 133 1/3 %.
I swear (right hand on the Fible) that I'll be more careful next time!

Originally Posted by Wilmer

Just a joke, n/0; I'm the one that missed something; I read this:
"He buys a suit and puts it on sale for 133 and 1/3 percent of it's wholesale price."
as a profit margin of 133 1/3 %.
I swear (right hand on the Fible) that I'll be more careful next time!

Right hand on the Fible! Well, it's not that serious..