Measured against what you started with

A pump costs ₹250. The price rises by 20%. Up by 20% of what?

The rule

It is 20% of the starting price, ₹250.

The base is the amount you start with. A rise or a fall is a percentage of the base. Add a rise. Subtract a fall.

There is a short way. A 20% rise keeps 100% and adds 20%. That is 120%, or times 1.2. A 20% fall leaves 80%, or times 0.8.

• ₹500 falls by 20%. 20% of 500 is 100. New price: 500 − 100 = ₹400.
• ₹500 × 0.8 = ₹400. The same answer.
• ₹6,400 with 5% tax (an extra charge on the price) added. 5% of 6,400 is 320. Total: 6,400 + 320 = ₹6,720.
• Short way: 6,400 × 1.05 = ₹6,720.

Sometimes you know the new amount and want the base.

• After 20% off, a lamp costs ₹360. That is 80% of the base.
• 80% is eight pieces of 10%. So 10% is 360 ÷ 8 = ₹45.
• The base is 45 × 10 = ₹450.
• 30% of the base is 45. So 10% is 45 ÷ 3 = 15.
• The base is 15 × 10 = 150.