The price (p) of a commodity is first increased by k%, then decreased by k%; again increased by k%, and again decreased by k%. If the new price is q, then what is the relation between p and q?

Correct Option (4)

Let the initial price of the commodity be p.

• After the first increase by k%, the price becomes:
• After the first decrease by k%, the price becomes:
• After the second increase by k%, the price becomes:
• After the second decrease by k%, the final price q becomes:

This expression can be simplified using the algebraic identity .

Applying this identity to the terms , we get:

.