An equal rise and fall do not cancel

A ₹250 price rises 20%. Then it falls 20%. Is it ₹250 again?

The rule

No. The price ends at ₹240, not ₹250. The fall does not undo the rise.

The second percentage is taken of the new amount, not the start. So an equal rise and fall do not cancel.

• Up 20%: 20% of 250 is 50, so 250 + 50 = 300.
• Down 20%: 20% of 300 is 60, so 300 − 60 = 240.
• Two discounts (cuts in price) on ₹500: 30%, then 20%.
• First, 30% of 500 is 150, so 500 − 150 = 350.
• Then 20% of 350 is 70, so 350 − 70 = 280.

The total cut is 500 − 280 = ₹220. And 220 ÷ 500 = 0.44. So 30% off, then 20% off, is 44% off. A single 50% discount gives 500 − 250 = ₹250. So it is not 50% off.

Try the lab to finish this lesson.