Martha bought an armchair and a coffee table at an action and sold bot

Responding to a pm:

Question: Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of the coffee table?

Pa - Gross profit on armchair
Pc - Gross profit on coffee table

We need to get (Pa - Pc)/Pc = (Pa/Pc - 1)

Pa = Sa - Ca = Selling price - Cost price of armchair
Pc = Sc - Cc = Selling price - Cost price of coffee table

We need to get (Sa-Ca)/(Sc - Cc) - 1

(1) Martha paid 10 percent more for the armchair than for the coffee table.

This means Ca = 1.1Cc

(2) Martha sold the armchair for 20 percent more than she sold the coffee table.

This means Sa = 1.2Sc

Both statements together give us (1.2Sc - 1.1Cc)/(Sc - Cc) which is still not enough. Hence answer is (E).

In case, instead, we had (1.1Sc - 1.1Cc)/(Sc - Cc) or (1.2Sc - 1.2Cc)/(Sc - Cc) etc, we could have taken the common factor out and cancelled it and we would have got 1.1 - 1 = 10% or 20% etc. In that case, answer would have been (C).

In essence, if the cost price of armchair is more than the cost price of coffee table by some percent x and if the selling price is also more by the same percent x, then the gross profit on the armchair would also be more by the same percent x.

Gross profit = Selling price - cost price
If selling price is 10% more and cost price is also 10% more, then the gross profit will be 10% more too.
New Gross Profit = 1.1*Selling price - 1.1*cost price = 1.1 * (Selling price - cost price) = 1.1*Gross profit