condition: to find the wholesale cost???
given: let wholesale cost be X
List price then will be 1.2 X (to be noted: we cannot assume that list price is equal to selling price)

stat 1: 0.9(1.2X)-X=10$ so 1.08X = 10 we can find X
stat 1 alone is sufficient

stat 2: sale = 50$ we do not know if sale price = list price hence we cannot find X. (how to cross check whether sale price equals the list price or not: if we assume 50$ in this case is also the list price, it will give us conficting answers for wholesale price which cannot be correct)
Therefore B alone is Not sufficient

answer should be A.

This is a DS algebra problem asking you to solve for the value of a variable so you can use the method of counting equations to see if you have the same number of equations as variables.
Start with translating the equation you get in the question stem:
P = 20/100(W)
Look at statement #1 - does it give you another equation with the same variables?
List price is really W +P (so not a new variable)

(W + P)*90/100= W+10 ( i did 90% so I would not have to subtract out the 10%) - yes this is a second equation with the same variables - no multiple equations and no exponents so you can use this to solve the problem - answers AD are left.

Check statment #2 The sold is a new variable - as the top equation only talks about listed cost, not selling cost - so you cannot use this equation.

The answer is A.

The trick to this problem is that you have to realize that list price is not a new variable - if you look at it as a counting variables problem then this is much easier to see.