Math Problem: Percentage Problem

[engmahbub091]

Question:

A collector purchased a work of art for x% less than the appraised value. He then sold the work to a private buyer for a profit of y%. Which of the following represents the price the private buyer paid, as a fraction of the appraised value?

Answer of this question is: 1 - (x/100) + (y/100) - (xy/10000)


Please explain this question, I mean logic behind the answer.

[tommywallach]

Hey Engma,

I would likely solve this question by plugging in values.

Let's call the appraised value $200

A collector purchased it for x% less. Let's make that 50%. So he purchased it for $100

He then sold the work for a profit of y%. Let's call that 25. So he sold it for $125.

The answer would then be 125/200, or 5/8.

Then you would plug into the answer choices. However, the answer you have listed is not the correct answer, so your question is wrong. Where did you find it?

-t

[bije1968]

original value = V: x percent is V/ 100* x= Vx/ 100 : it purchased for amount of money which I show as V - Vx / 100 it means (100V-Vx) / 100 , ok? then, it sold for y% more than it purchased, it means should multiply to y/100 because it is % and add to the previous amount , so (100V- Vx) / 100* y/100 + (100V-Vx) / 100= (100Vy- Vxy) / 10000+ (100V-Vx) / 100= (100 Vy - Vxy+ 1000V- 100x) /10000 = V (100 y - xy +10000 - 100x) / 1000 is buyer paid, now find fraction of original value V, so devide by V youll get
(100y- xy+1000 - 100x)/10000 = y /100 - xy / 10000 + 1 - x/100 same as your answer 1 - (x/100) + (y/100) - (xy/10000)
Write all of it on a paper as a fraction to get easier GOOD LUCK to you and me!!! )))))))

[tommywallach]

Just a side note. My method DOES get the answer he posted. (Did the subtraction as addition in my head!). I think we can all agree, my way is way better. Plug in on questions with variables in the answer choices. It's better!

-t