If the price of a television set is increased by 25%. then by what percentage should the new price be reduced to bring the price back to the original level ?

Let the original price be P. After a 25% increase the new price becomes 1.25P. To return to the original price we must find the percentage reduction from 1.25P down to P: reduction = (1.25P − P)/1.25P = 0.25P/1.25P = 1/5 = 0.20, i.e. 20%. Equivalently, the item is at 125% of its original value after the increase, so we need to reduce 125% to 100%, a fall of 25 percentage points on a 125% base: (25/125)×100 = 20%. This is a straightforward reverse-percentage calculation as described in basic reverse-percentage methods.