A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:

Answer: Option B

First Method
Let CP was 100 for A originally
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110
Now, B sells it A again with loss 10%
Now, CP for A this time = 110 - 10% of 110 = 99
A makes Profit = 110 - 99 = 11
%profit for A = $$\frac{11\times 100}{100}$$  = 11%

Second Method
It could be easily shown by net percentage change graphic.
100(A) == 10%(Profit) ⇒110(B) == 10%(Loss) ⇒ 99(A)

In this transaction A makes a profit of (110 - 99 = 11%) 11%

[10% on selling to B and 1% profit on buying back from B]