Reverse percentages: how to find the original number
A reverse percentage question gives you a figure after a percentage rise or fall and asks for the figure before it. Divide the figure you have by the multiplier, which is 1 plus the rise or 1 minus the fall, written as a decimal.
Taking the percentage off the figure you have, or adding it back on, gives the wrong answer. The percentage was worked out on the figure before the change, which the question does not give you.
This drill gives you five untimed questions that each work back from a price rise, free to use with no sign-up, and each one is worked through after you submit.
5 questions · untimed · free to use · no sign-up
One question of this type, worked in full
Try the question before you read on. The steps take the fastest route that still shows the reasoning, and the last one is the answer the drill marks.
A software licence costs 360 euros a year after a price rise of 20 percent. What did the licence cost a year before the rise?
- The 20 percent rise was worked out on the price a year before, so 360 euros is 100 + 20 = 120 percent of that price.
- As a multiplier, 120 percent is 120 ÷ 100 = 1.20.
- Divide the price you are given by the multiplier: 360 ÷ 1.20 = 300 euros.
Answer: 300 euros. Testonome practice pace: 65 seconds for a question like this.
Check it forward: 300 × 1.20 = 360 euros, the price the question gives.
After a fall, the method is the same
Some questions give the figure after a fall instead of a rise. The fall was also worked out on the original, so you divide by what is left of it. The five questions in this drill all work back from a rise, so this example sits here rather than in the set. Try it before you open the working.
A supplier's quote comes to 640 euros after a 20 percent discount. What was the price before the discount?
Show the working
- The 20 percent discount was worked out on the full price, so 640 euros is 100 − 20 = 80 percent of that price.
- As a multiplier, 80 percent is 80 ÷ 100 = 0.80.
- Divide the price you are given by the multiplier: 640 ÷ 0.80 = 800 euros.
Answer: 800 euros.
Check it forward: 800 × 0.80 = 640 euros, the price the question gives.
Four ways this question type goes wrong
Each question offers these alongside the right answer, and the review names which one you took.
Off the new price
Taking the percentage off the price after the rise, which works it out on the wrong figure.
Rise added again
Putting the rise on a second time instead of undoing it, which moves further from the answer.
Percent taken as euros
Subtracting the percentage as though it were an amount of money.
The rise alone
Giving how much the price went up by, when the question asks what it cost before.
What the review gives you after you submit
You get the working for every question, the answer you chose beside the right one, and the reason the option you picked is wrong. Nothing is sent anywhere while you work.
5 questions · untimed · free to use · no sign-up
Other numerical skills you can drill
The reverse percentage formula, beside the other numerical formulas