A price first went up 50%, then next month came down 50%

Why

Up 50 then down 50 sounds like it cancels, and Ravi's right that they're the same SIZE of percent. The trap is that each percent is taken from a DIFFERENT price. The rise is 50% of the small starting price; the fall is 50% of the bigger raised price — so the fall removes more rupees than the rise added. Try ₹100: up 50% makes ₹150; then 50% of ₹150 is ₹75 off, leaving ₹75 — below where it began. The percentages match, the amounts don't, because the second acts on a larger base. Test: same idea as a discount stacked on a raised tag — the second cut bites a bigger number. It is now lower: equal up-and-down percentages don't return to the start, because each works on a different-sized price.