# Simple Percentage Logic

• Sep 28th 2010, 10:28 PM
99.95
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?"
Edit: note, percentage loss refers to the amount harry lost by selling it back for a lower price
• Sep 29th 2010, 05:52 AM
Wilmer
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%
• Sep 29th 2010, 06:06 AM
99.95
incorrect :D
• Sep 29th 2010, 06:16 AM
undefined
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.
• Sep 29th 2010, 06:32 AM
Wilmer
Well, ain't spending time looking for a play on words;

.57142... * 280 = 160, which is what he lost: 280 - 120 = 160
• Sep 29th 2010, 06:35 AM
99.95
would 's' not be equal to 1 + 1/3 ?
(Undefined is correct)
• Sep 29th 2010, 07:55 AM
Wilmer
Quote:

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
• Sep 29th 2010, 08:05 AM
undefined
Quote:

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.
• Sep 29th 2010, 08:17 AM
Wilmer
Quote:

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?
• Sep 29th 2010, 08:36 AM
undefined
Quote:

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?
• Sep 29th 2010, 12:40 PM
Wilmer
Quote:

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!
• Sep 29th 2010, 12:52 PM
undefined
Quote:

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.. :)