Revision notes
Work out new prices after a percentage rise or fall, and find the percentage change between an old and a new price.
Emeka pays ₦500 for the bus to school. One Monday the conductor shouts, "Fare don increase by 20%!" How much must Emeka pay now — and if the fare later drops back by 20%, does it return to ₦500? Percentages give the answer.
A percentage increase or decrease is always a percentage of the old (original) amount.
Emeka's fare: 20% of ₦500 = 20100 × 500 = ₦100. The fare went up, so the new fare is ₦500 + ₦100 = ₦600.
If a ₦2,000 bag drops by 25%, the decrease is 25100 × 2,000 = ₦500, so the new price is ₦2,000 − ₦500 = ₦1,500.
🔑 Key idea: Find the % of the OLD amount, then add it (increase) or subtract it (decrease).
The old amount is 100%. After a 20% increase you have 100% + 20% = 120% of it, and 120% = 1.2. So ₦500 × 1.2 = ₦600 in one step.
After a 25% decrease you have 100% − 25% = 75% = 0.75. So ₦2,000 × 0.75 = ₦1,500.
Careful: 20% up and then 20% down does not get you back to the start, because the second 20% is of a different, bigger amount: ₦600 × 0.8 = ₦480.
🔑 Key idea: Increase by p% → multiply by (100 + p)%. Decrease by p% → multiply by (100 − p)%.
If you know the old and new prices, first find the change (the difference).
Then compare it with the old price: percentage change = change ÷ old price × 100.
Rice goes from ₦40,000 to ₦50,000: change = ₦10,000, and 10,000 ÷ 40,000 × 100 = 25% increase. Dividing by the new price (₦50,000) would wrongly give 20%.
🔑 Key idea: Percentage change = change ÷ OLD amount × 100.
A football cost ₦600. The price went up by 40%. What is the new price?
Step 1: Find 40% of the old price
40100 × 600 = ₦240
Step 2: Add the increase
₦600 + ₦240 = ₦840
Step 3: Or in one step
140% of ₦600 = 1.4 × 600 = ₦840
Why? The new price is 100% + 40% of the old price.
Answer: ₦840
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