A share bought for ₹200 rose by 100 percent during the first year and then fell by 50 percent during the second year. What was the average annual percentage change in its price over the two years?

Percentage changes must be compounded, not averaged, because each one is measured against a different base. The price runs ₹200 → ₹400 after the 100 percent rise → ₹200 after the 50 percent fall, because that fall is 50 percent of ₹400, not of ₹200. The share ends exactly where it began, so the average annual change is 0 percent. The trap is 25 percent, the plain average of +100 and −50, which quietly treats both changes as though they applied to the same ₹200 base; if that were right the share would be worth ₹312.50 today. The value 50 percent is the size of the fall read as though it were the overall outcome, and −50 percent takes the second year's figure alone as the average. Note that the answer does not depend on the ₹200 at all — any starting price doubles and then halves back to itself.