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11+ Percentages of Amounts: Questions and Worked Answers
Find percentages using 10%, 1% and fraction shortcuts, then tackle discounts and money questions with three examples and six original practice questions.
A percentage describes an amount in hundredths. The symbol % means “per hundred”, so 35% means 35 out of every 100 equal parts. To find 35% of an amount, you need to find the value of those parts for that particular whole.
Suggested difficulty: foundation to intermediate, with one stretch question. These are editorial estimates. You will need division by 10 and 100, multiplication and basic fractions. These original questions teach the method; they are not official past-paper questions or a prediction of a particular school’s exam.
Start with useful building blocks
To find 10% of an amount, divide it by 10. To find 1%, divide it by 100. You can combine these amounts to make the percentage you need: 30% is three lots of 10%; 5% is half of 10%; 15% is 10% plus 5%.
For example, if the whole is 240, then 10% is 24 and 1% is 2.4. The percentage remains the same kind of relationship whatever the whole is. But 10% of 240 and 10% of 80 are different amounts, because they start from different wholes.
Do not round your building blocks too early. If 1% is a decimal, keep that value while calculating. For money, write the final amount clearly in pounds and pence, or in pence throughout.
Use a fraction when it is simpler
50% is 1/2, so halve the amount. 25% is 1/4, so divide by four. 75% is 3/4, so find one quarter and multiply by three. These are different ways of writing the same relationships, not separate rules to memorise without understanding.
For a stretch calculation, 12.5% is 1/8 because it is half of 25%. You can find 12.5% by dividing by eight, or by finding a quarter and halving it. Use the method whose arithmetic feels clearest for the numbers in front of you.
Any percentage: the 1% method
For a whole-number percentage such as 17%, find 1% and multiply it by 17. Alternatively, combine 10%, 5% and 2%. Both methods work because you are adding equivalent portions of the same whole.
A useful check for a percentage between 0% and 100% is that the answer lies between zero and the whole positive amount. A percentage above 100% can produce a larger answer; for example, 150% means one and a half times the amount.
Discount amount or final price?
A 20% discount is the amount taken off, not the price paid. If the question asks for the sale price, first calculate the discount and subtract it from the original price. Alternatively, calculate the 80% that remains.
An increase works in the other direction: add the calculated increase to the original amount. Read the last line carefully. “Find 20% of the price” and “find the price after 20% off” request different answers.
What this lesson does not cover
Finding what percentage one amount is of another and recovering an original price after a percentage change are separate skills. Do not automatically reuse this method without identifying the whole. If a reduced price is given, that price may represent less than 100% of the original.
Work through the practice before looking at the explanations. If you get an answer wrong, identify whether the error was choosing a percentage method, doing the arithmetic or answering the wrong part of the question. Try the calculation again with the whole and requested amount labelled.
Worked examples
Example 1: Find 35% of 180.
- 10% of 180 is 18.
- 30% is 3 × 18 = 54, and 5% is half of 18 = 9.
- 35% is 54 + 9 = 63.
- Check: 35% is more than a quarter but less than a half. The answer 63 is between 45 and 90.
Answer: 63
Example 2: A coat costs £64 before a 25% discount. What is the sale price?
- 25% is one quarter, so the discount is £64 ÷ 4 = £16.
- Subtract the discount from the original price: £64 − £16 = £48.
- Check: the price paid is the remaining 75%, not the £16 saving.
Answer: £48
Example 3: Find 7% of £250.
- 1% is £250 ÷ 100 = £2.50.
- 7% is 7 × £2.50 = £17.50.
- Check: 10% would be £25, so a 7% amount should be less than £25.
Answer: £17.50
Common mistakes to avoid
- Writing the percentage number as the amount. 30% of 70 is 21, not 30.
- Dividing by the percentage. To find 20%, find one fifth or build it from 10%; do not divide the amount by 20.
- Giving the saving instead of the sale price. Subtract the discount when the question asks what you pay.
- Losing place value when dividing by 100. £250 ÷ 100 is £2.50, not £25.
- Comparing percentages without checking their wholes. A larger percentage of a smaller amount can still be less money.
Try it yourself
Write down your working before opening each answer. If you make a mistake, check the explanation and try the question again.
1. Find 20% of 85.
Show answer and explanation for question 1
Answer: 17
10% is 8.5. Double that to get 20%: 8.5 × 2 = 17. Alternatively, 20% is one fifth, and 85 ÷ 5 = 17.
2. Find 75% of 92.
Show answer and explanation for question 2
Answer: 69
25% is one quarter: 92 ÷ 4 = 23. Three quarters is 23 × 3 = 69.
3. Find 6% of £350.
Show answer and explanation for question 3
Answer: £21
1% is £3.50. Six lots of £3.50 equal £21.
4. A bag originally costs £80. Its price is reduced by 15%. What is the new price?
Show answer and explanation for question 4
Answer: £68
10% is £8 and 5% is £4, so the discount is £12. The new price is £80 − £12 = £68.
5. Which is greater: 40% of 65 or 30% of 90? By how much?
Show answer and explanation for question 5
Answer: 30% of 90 is greater by 1.
40% of 65 is 4 × 6.5 = 26. 30% of 90 is 3 × 9 = 27. The smaller percentage gives the larger amount here because the whole is larger.
6. Stretch: A tank holds 72 litres when full. It currently contains 12.5% of its capacity. How many more litres are needed to fill it?
Show answer and explanation for question 6
Answer: 63 litres
12.5% is one eighth, so the tank contains 72 ÷ 8 = 9 litres. It needs 72 − 9 = 63 more litres. The question asks for the missing amount, not the amount already inside.
Sources and context
The questions and worked examples on this page are original practice material, not official past-paper questions. Exam requirements vary by school and entry year.