Did the seller earn a profit?

Explanation from the source:

Let c and s be the cost and the selling price, respectively, for the seller on each item.

From Statement (1) alone, we have that the selling price of 20 items equals the cost of 15 items.
Hence, we have 20s = 15c, or s = (\(\frac{15}{20}\))c = \(\frac{3c}{4}\).
Now, profit = selling price – cost = s – c = \(\frac{3c}{4}\) – c = \(\frac{–c}{4}\), a negative value (c is price and therefore is positive. Hence, –c/4 is negative).
A negative profit should be considered a loss. Hence, Statement (1) alone is sufficient to determine that the seller did not earn a profit.

From Statement (2) alone, we have that the cost of 10 items is $55 more than the selling price of 8 items.
The cost of 10 items is 10c and the selling price of 8 items is 8s.
Hence, we have 10c – 8s = 55.
Subtracting 2s from both sides yields 10c – 10s = 55 – 2s; 10(c – s) = 55 – 2s; c – s = \(\frac{(55 – 2s)}{10}\).
Now, if 55 – 2s is positive, c – s, which equals \(\frac{(55 – 2s)}{10}\), is positive. Here, Cost > Selling Price, and seller made a profit.
Otherwise, he did not make a profit. 55 – 2s is not positive if s < 55/2.
Hence, we have a double case and Statement (2) alone is not sufficient.