What happens with profit if prices increase by 10 pct and volume decrease by 10 pct?
I guess the sales are determined as $$ TR = P \cdot Q, $$ so the changes results in $$ TR' = (1.1 \cdot P) \cdot (0.9 \cdot Q) = 1.1 \cdot 0.9 \cdot TR = 0.99 \cdot TR, $$ so the sales decrease by 1 pct.
Is this the correct answer? If volume decrease by 10 pct, I would assume that the costs are also affected if there are variable costs.
How do I answer this question correctly?
You can also find $d(TR) = QdP + P.dQ$
For all practical purpose, your calculation is right. But this is one other way, I have given an example of 10 percent increase in Price and 10 percent decrease in volume and used the above formula to derive the change in Revenue. Here we assume that cost is not affected.
$P_0 = 100, P_1 = 110, Q_0 = 10, Q_1 = 9$
$TR_0 = 1000, TR_1 = 990 , d(TR) = -10$
Using the forumula $=100(9-10)+9(110-100) = -10$