Is it possible that the percentages can be negative?

Question

Can we have the percentages as negative? Is percentages always a positive number? Recently, I was solving the algebraic question, and it boils down to $n^2 = 100$. Here, $n$ was the percentage - So, there can be two answers here $ 10$ or $-10$. So, my doubt is that can percentage be negative. I understand that percentages are basically ratios. Since ratios can be negative, is it possible that percentages can be negative too.

Answer 1

Consider a question where you sell a product where the CP=75 and SP=100 so the change (profit or loss) =$25$(SP-CP) since SP>CP it is profit and if CP were less than SP than it would have been loss

so now you are asked to find the profit percentage

To find the profit percentage $\frac {SP-CP}{CP} *100$ that

if SP is greater than CP than you get the profit percentage if SP is less than CP than you would get the fraction negative and you take it as a loss percentage so the negative sign indicates that it is a loss.

Now again if you were asked to find the fractional change or percentage in value of some variable then the variable might increase or decrease and accordingly your percentage might become positive or negative.

Hope this helped