A vendor increases the price of an item by x% of its cost price to det

Question

A vendor increases the price of an item by x% of its cost price to determine the selling price. However, when the item does not sell, he offers a discount of y% on the selling price. As a result, on the sale of the item at the current price he neither makes a profit nor incurs a loss on the transaction. Select the two values of x and y from the table that are consistent with the given conditions. Source : http://www.GMATinsight.com LINK for more TPA questions

ccarson · Answer

Pretty straightforward and simple, you can just plug in values until you get the right answer.

You can also think of it as in fractions as well. 
First think of it starting at 100/100, the original cost. An increase of 25/100 would mean the fraction goes to 125/100 or 5/4. 
Take the reciprocal (4/5) in order to figure out which discount brings the selling price back to its original cost. 20/100 or 4/5 fits this perfectly. 
Therefore, x = 25 and y = 20.

punwani7 · Answer

Bunuel  Can you help me out with a different approach for this?

varun017 · Answer

formula for calculating the net percentage change is a +b +ab/100 where a and b are percentage change,

Here as there is a discount so we will take b as negative

by using permutation we can observe taking a = 25 and b = - 20 we get 0

25-20+(25x-20)/100 = 5-5 => 0

LessGoRahul · Answer

Let the  cost price (CP) = 100 .
The vendor marks it up by x%, so:
SPmarked=100+x
Then he gives a discount of y%, so the final selling price is:
(100+x)(1−100y)
Since he makes  neither profit nor loss , final SP = CP = 100:
(100+x)(1−100y)=100
Rearrange:
(100+x)(100−y)=10000 10000−100y+100x−xy=10000 100x=100y+xy x(100−y)=100y
Therefore:
x=100−y100y

x	y	Statement
		15
		20
		25
		30
		35
		40

A vendor increases the price of an item by x% of its cost price to det

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GMAT Two-part Analysis (TPA) Questions

A vendor increases the price of an item by x% of its cost price to det

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