Sorry Sir.

There was two versions of the same question.

The one I posted had a constant in the stem.

I have edited the question see above .

In your case without the editing yes you are right the answer would be D

Great job

+ kudo

Thanks Carcass for the swift response!

In this case y - x > x - y

it would mean 2 y > 2x
hence y > x

and as per my previous example

Algebraically we have (1-x%) * (1+y%) > (1+x%) (1-y%)

Since the percentage increase from x is smaller than the percentage increase from y it would make the answer choice A

As an example x = 10% and y = 20%

0.9 * 1.2 > 1.1 * 0.8

Here the answer choice is A

My Pleasure Sir

From the above inequality, we get y>x .
suppose y is 20% , x is 10% and original price was 100$.

Here in quantity A,
The price of the item if the 100 $ original price were decreased by 10 % , increased by 35%, and then increased by 20%,
hence, price after all percentage = 100*0.90*1.35*1.20 ........(increment by 10 % means original price is supposed to multiply by 1.10, thats why i did this to save time)

But in Quantity B,
The price of the item if the original price 100 $ were increased by 10 % , decreased by20 %, and then increased by 35 %

The final price of the item = 100*1.10*0.80*1.35.
Since, in both quantity, 100*1.10*1.35 is common and we left with 0.90 in Quantity A and 0.80 in Quantity B.

Hence answer is A.
PM me or comment here if doubts remain.

okay since the question is on percentages should we assume that both x and y are positive and solve the equation cause if the numbers are negative we cant just take it to left side and solve equation right??

Of course. If we deal with % the number of starting point are somehow positive.