Percentage chapter concept of 11 plus exam,
Part 1: Step-by-Step Guide to Percentages for the 11+
What is a Percentage?
"Percent" means "out of 100". The symbol is
%.So, 25% means 25 out of 100, or
25/100.
Step 1: Finding a Percentage of an Amount (The Most Common Question)
Method 1: Find 1% First (The Safest Method)
Find 1% of the amount by dividing it by 100.
Multiply this answer by the percentage you need.
Example: Find 15% of £80.
1% of £80 = £80 ÷ 100 = £0.80
15% = 15 × £0.80 = £12
Method 2: Use a Decimal Multiplier
Convert the percentage to a decimal by dividing by 100.
Multiply this decimal by the amount.
Example: Find 15% of £80.
15% ÷ 100 = 0.15
0.15 × £80 = £12
Method 3: Use Fractions (Good for mental maths)
Convert the percentage to a fraction and multiply.
15% = 15/100 = 3/20
(3/20) × £80 = (3 × £80) / 20 = £240 / 20 = £12
Step 2: Expressing One Number as a Percentage of Another
Formula: (Part ÷ Whole) × 100
Example: What percentage is 12 out of 40?
(12 ÷ 40) = 0.3
0.3 × 100 = 30%
Step 3: Percentage Increase
Formula: New Amount = Original Amount × (1 + Percentage/100)
Example: Increase £60 by 5%.
Method A: Find 5% and add it on.
5% of £60 = £3
£60 + £3 = £63
Method B: Use the multiplier.
A 5% increase means you have 105% of the original (100% + 5%).
105% = 1.05
£60 × 1.05 = £63
Step 4: Percentage Decrease
Formula: New Amount = Original Amount × (1 - Percentage/100)
Example: Decrease £80 by 12%.
Method A: Find 12% and take it away.
12% of £80 = £9.60
£80 - £9.60 = £70.40
Method B: Use the multiplier.
A 12% decrease means you have 88% of the original (100% - 12%).
88% = 0.88
£80 × 0.88 = £70.40
Step 5: Reverse Percentages (Finding the Original Amount)
This is a harder topic that often appears. You are given the final amount after a percentage change and must find the original amount.
Key Idea: Work backwards from the multiplier.
Example: After a 20% discount, a book costs £10. What was the original price?
A 20% discount means you paid 80% of the original price (100% - 20%).
So,
80% of Original Price = £100.8 × Original Price = £10To find the Original Price, do the opposite of multiplying by 0.8, which is dividing by 0.8.
Original Price = £10 ÷ 0.8 = £12.50
Check: 20% of £12.50 is £2.50. £12.50 - £2.50 = £10. Correct!
Part 2: Practice Questions (from the style of GL Assessment)
Here are 45 questions covering all sub-topics. The first 10 are in the style of previous GL 11+ questions.
10 Questions in the GL/Slough Consortium Style
Calculate 30% of 250 metres.
A shirt costs £35. In a sale, everything is reduced by 15%. What is the sale price of the shirt?
In a class of 30 children, 18 are girls. What percentage of the class are girls?
A packet of biscuits has 10% extra free. The packet now contains 66 biscuits. How many biscuits were there in the original packet?
Increase 240 by 12.5%.
Sam scores 72 out of 80 in a test. What is his percentage score?
A town's population of 20,000 increased by 5% one year and then decreased by 5% the next year. What was the population after the two years?
In a box of fruits, 40% are apples, 25% are oranges, and the rest are bananas. What percentage are bananas?
A computer game was £50. Its price was reduced by £7.50. What is this reduction as a percentage?
A coat's price is increased by 20% to £90. What was the original price?
35 More Questions on All Sub-Topics
Finding a Percentage of an Amount:
11. Find 45% of 600 kg.
12. What is 7% of £300?
13. Calculate 12.5% of 80 litres.
14. Work out 100% of 24.
15. Find 1% of 4 kilometres.
Expressing as a Percentage:
16. What percentage is 15p of £1? (Hint: Use the same units! £1 = 100p)
17. What percentage is 8 cm of 40 cm?
18. What percentage is 36 out of 60?
19. A student gets 47 marks out of 50 in a science test. What percentage is this?
20. A pizza is cut into 8 slices. If 3 slices are eaten, what percentage of the pizza is left?
Percentage Increase:
21. Increase 400 by 23%.
22. Increase £65 by 100%.
23. A salary of £40,000 is increased by 3%. Find the new salary.
24. The number 80 is increased by 25%. Find the new number.
25. Increase 120 by 5%, then by a further 10%.
Percentage Decrease:
26. Decrease 900 by 18%.
27. Decrease £120 by 5%.
28. A phone priced at £180 is reduced in a sale by 30%. Find the sale price.
29. The temperature was 20°C. It fell by 35%. Find the new temperature.
30. Decrease 150 by 10%, then by a further 20%.
Reverse Percentages:
31. After a 10% pay rise, Jane's salary is £33,000. What was her original salary?
32. In a sale, a jacket is reduced by 15% to £42.50. What was the original price?
33. The price of a holiday is increased by 8% to £810. What was the original price?
34. A tank of water loses 30% of its volume, leaving 140 litres. How much water was in the tank originally?
35. After eating 30% of a box of chocolates, 21 chocolates remain. How many were in the box originally?
Multi-Step and Word Problems:
36. A bike costs £320. VAT at 20% is added. What is the total cost?
37. In a school, 60% of the 450 students are boys. How many girls are there?
38. A shop buys cakes for £1.50 each and sells them for £2.40. What is the percentage profit?
39. A number is increased by 20% and then the result is decreased by 20%. Is the final number greater than, less than, or equal to the original number? Show your working.
40. In a recipe, 40% of the mass is flour, 35% is sugar, and the rest is butter. If the butter weighs 150g, what is the total mass of the recipe?
41. A company's profits were £80,000. This was a 25% increase on the previous year. What were the profits the previous year?
42. A library has 12,000 books. 45% are fiction, and 1/3 of the fiction books are science fiction. How many science fiction books are there?
43. A car depreciates in value by 15% each year. If it was bought for £12,000, what is its value after one year?
44. In a sports club, 70% of the members are adults. The rest are children. There are 45 children. How many members are there in total?
45. A bag contains red, blue, and green counters. 25% are red. The ratio of blue to green counters is 4:5. If there are 45 green counters, how many counters are in the bag?
Answers
GL/Slough Style Questions (1-10):
75 m
£29.75
60%
60 biscuits
270
90%
19,950
35%
15%
£75
Additional Questions (11-45):
11. 270 kg
12. £21
13. 10 litres
14. 24
15. 0.04 km (or 40 m)
16. 15%
17. 20%
18. 60%
19. 94%
20. 62.5%
21. 492
22. £130
23. £41,200
24. 100
25. 138.6
26. 738
27. £114
28. £126
29. 13°C
30. 108
31. £30,000
32. £50
33. £750
34. 200 litres
35. 30 chocolates
36. £384
37. 180 girls
38. 60%
39. Less than (e.g., 100 -> 120 -> 96)
40. 600g
41. £64,000
42. 1,800 books
43. £10,200
44. 150 members
45. 100 counters
MATHS:
35% of 420 = ?
Increase 180 by 15% = ?
The ratio of boys to girls is 3:4. If there are 21 boys, how many girls?
Solve: 4x - 7 = 21
Find the area of a triangle with base 12cm and height 8cm
NVR:
Look for patterns in these sequences mentally:
Square → Rotated square → Rotated square → ?
Light shading → Medium shading → Dark shading → ?
1 line → 2 lines → 3 lines → ?
Percentage Practice Questions (GL Assessment Style)
Set 1: Finding a Percentage of an Amount (10 Questions)
Find 20% of 350 kg.
Calculate 15% of £80.
What is 75% of 48 metres?
Work out 5% of 240.
Find 12.5% of 400.
Calculate 32% of £150.
What is 8% of 625 ml?
Find 100% of 37.
Calculate 17.5% of 200.
What is 1% of 8.4 km?
Set 2: Expressing One Number as a Percentage of Another (10 Questions)
What percentage is 18 out of 50?
What percentage is 35p of £1? (Remember: £1 = 100p)
In a test, Sarah scored 42 out of 60. What is her percentage score?
A class has 30 students. 12 of them are left-handed. What percentage is left-handed?
What percentage is 120 g of 2 kg? (Hint: 2 kg = 2000 g)
A pizza is cut into 8 slices. If 3 slices are eaten, what percentage of the pizza remains?
What percentage is 15 minutes of 1 hour?
A bag contains 20 sweets. 8 are red. What percentage are not red?
Express 7 as a percentage of 28.
A football team played 20 games and won 14. What percentage of games did they win?
Set 3: Percentage Increase (10 Questions)
Increase 400 by 12%.
Increase £65 by 20%.
A salary of £42,000 is increased by 3%. Find the new salary.
The number 250 is increased by 18%. Find the new number.
Increase 80 by 7.5%.
A library had 12,000 books. The number of books increased by 15% after a donation. How many books does it have now?
Increase 1,440 by 10%.
The price of a £30,000 car is increased by 8.5%. Find the new price.
Increase 56 by 25%.
A container holds 600 litres of water. The volume increases by 4%. How much water is there now?
Set 4: Percentage Decrease (10 Questions)
Decrease 700 by 14%.
Decrease £120 by 15%.
A phone priced at £450 is reduced in a sale by 30%. Find the sale price.
The temperature was 25°C. It fell by 16%. Find the new temperature.
Decrease 1,800 by 12.5%.
A tree was 5 metres tall. Its height decreased by 8% in a storm. What is its new height?
Decrease 92 by 75%.
A shop reduces all prices by 5%. If a jacket was originally £85, what is its new price?
Decrease 1,250 by 1%.
A battery's charge was 8,000 mAh. It has lost 22% of its charge. How much charge remains?
Set 5: Reverse Percentages (10 Questions)
After a 10% pay rise, David's salary is £38,500. What was his original salary?
In a sale, a table is reduced by 20% to £160. What was the original price?
The price of a bike is increased by 8% to £486. What was the original price?
After a 15% discount, a book costs £10.20. What was the price before the discount?
A tank of water loses 40% of its volume, leaving 180 litres. How much water was originally in the tank?
After eating 35% of a packet of biscuits, 39 biscuits are left. How many biscuits were there originally?
A town's population increased by 5% and is now 94,500. What was the original population?
After a 12.5% decrease, a number is 70. What was the original number?
The value of a car depreciated by 18% and is now £12,300. What was its original value?
After a 6% tax is added, a meal costs £21.20. What was the cost before tax?
Set 6: Multi-Step and Word Problems (15 Questions)
A coat costs £120. VAT at 20% is added. What is the total cost?
In a school of 600 pupils, 55% are boys. How many girls are there?
A shop buys cakes for £2 each and sells them for £3.50. What is the percentage profit?
A number is increased by 10% and then the result is decreased by 10%. Is the final number greater than, less than, or equal to the original number? Prove it with an example.
In a recipe, 45% of the mass is flour, 30% is fruit, and the rest is sugar. If the fruit weighs 240g, what is the total mass of the recipe?
A company's profits were £120,000. This was a 20% increase on the previous year. What were the profits the previous year?
A laptop is priced at £800. It is reduced by 15% in a sale. A week later, the sale price is reduced by a further 10%. What is the final price of the laptop?
In a sports club, 60% of the 250 members are adults. The rest are children. 40% of the children are girls. How many boys are in the club?
A bank charges 5% interest per year on loans. If you borrow £2,000, how much will you owe after one year?
A carton contains 500 ml of juice. Sheena drinks 30% of it. How many millilitres are left?
In a year, a tree's height increased from 2.5 m to 2.8 m. What was the percentage increase?
A bag contains red, blue, and green counters. 20% are red. The ratio of blue to green counters is 3:5. If there are 30 green counters, how many counters are in the bag?
A TV was priced at £600. It was reduced by 10%. For the final weekend of the sale, the price was reduced again, and the TV sold for £459. What was the percentage reduction in the final weekend sale?
In a class, 70% of students passed a Maths test. 60% of the class passed an English test. Every student passed at least one test. What is the minimum percentage of students who passed both tests?
An item costs £200. The price is increased by 25%. A customer has a loyalty card that gives 10% off the final price. How much does the customer pay?
Answer Key & Solutions
Set 1: Finding a Percentage of an Amount
70 kg (350 ÷ 100 = 3.5; 3.5 × 20 = 70)
£12 (80 ÷ 100 = 0.8; 0.8 × 15 = 12)
36 m (48 ÷ 100 = 0.48; 0.48 × 75 = 36)
12 (240 ÷ 100 = 2.4; 2.4 × 5 = 12)
50 (12.5% = 1/8; 400 ÷ 8 = 50)
£48 (150 ÷ 100 = 1.5; 1.5 × 32 = 48)
50 ml (625 ÷ 100 = 6.25; 6.25 × 8 = 50)
37 (100% means the whole amount)
35 (17.5% = 17.5/100 = 7/40; 200 ÷ 40 = 5; 5 × 7 = 35)
0.084 km (8.4 ÷ 100 = 0.084)
Set 2: Expressing as a Percentage
36% (18/50 = 36/100 = 36%)
35% (35p/100p = 35/100 = 35%)
70% (42/60 = 7/10 = 70/100 = 70%)
40% (12/30 = 4/10 = 40%)
6% (120g/2000g = 12/200 = 6/100 = 6%)
62.5% (5 slices left / 8 total = 5/8 = 0.625 = 62.5%)
25% (15 min/60 min = 1/4 = 25%)
60% (12 not red / 20 total = 12/20 = 60/100 = 60%)
25% (7/28 = 1/4 = 25%)
70% (14/20 = 7/10 = 70%)
Set 3: Percentage Increase
448 (400 × 1.12 = 448)
£78 (65 × 1.20 = 78)
£43,260 (42,000 × 1.03 = 43,260)
295 (250 × 1.18 = 295)
86 (80 × 1.075 = 86)
13,800 books (12,000 × 1.15 = 13,800)
1,584 (1,440 × 1.10 = 1,584)
£32,550 (30,000 × 1.085 = 32,550)
70 (56 × 1.25 = 70)
624 litres (600 × 1.04 = 624)
Set 4: Percentage Decrease
602 (700 × 0.86 = 602)
£102 (120 × 0.85 = 102)
£315 (450 × 0.70 = 315)
21°C (25 × 0.84 = 21)
1,575 (1,800 × 0.875 = 1,575)
4.6 m (5 × 0.92 = 4.6)
23 (92 × 0.25 = 23)
£80.75 (85 × 0.95 = 80.75)
1,237.5 (1,250 × 0.99 = 1,237.5)
6,240 mAh (8,000 × 0.78 = 6,240)
Set 5: Reverse Percentages
£35,000 (Original × 1.10 = 38,500; Original = 38,500 ÷ 1.10 = 35,000)
£200 (Original × 0.80 = 160; Original = 160 ÷ 0.80 = 200)
£450 (Original × 1.08 = 486; Original = 486 ÷ 1.08 = 450)
£12 (Original × 0.85 = 10.20; Original = 10.20 ÷ 0.85 = 12)
300 litres (Original × 0.60 = 180; Original = 180 ÷ 0.60 = 300)
60 biscuits (Original × 0.65 = 39; Original = 39 ÷ 0.65 = 60)
90,000 (Original × 1.05 = 94,500; Original = 94,500 ÷ 1.05 = 90,000)
80 (Original × 0.875 = 70; Original = 70 ÷ 0.875 = 80)
£15,000 (Original × 0.82 = 12,300; Original = 12,300 ÷ 0.82 = 15,000)
£20 (Original × 1.06 = 21.20; Original = 21.20 ÷ 1.06 = 20)
Set 6: Multi-Step and Word Problems
£144 (120 × 1.20 = 144)
270 girls (100% - 55% = 45% girls; 600 × 0.45 = 270)
75% profit (Profit = £1.50; % Profit = (1.50/2.00) × 100 = 75%)
Less than (e.g., 100 → 110 → 99. The 10% decrease is applied to a larger number than the 10% increase).
800g (30% = 240g, so 1% = 8g; 100% = 800g)
£100,000 (Original × 1.20 = 120,000; Original = 120,000 ÷ 1.20 = 100,000)
£612 (First reduction: 800 × 0.85 = £680; Second reduction: 680 × 0.90 = £612)
60 boys (Adults: 250 × 0.60 = 150; Children: 250 - 150 = 100; Girls: 100 × 0.40 = 40; Boys: 100 - 40 = 60)
£2,100 (2,000 × 1.05 = 2,100)
350 ml (100% - 30% = 70% left; 500 × 0.70 = 350 ml)
12% increase (Increase = 0.3m; % Increase = (0.3/2.5) × 100 = 12%)
100 counters (Red = 20%. Blue + Green = 80%. Ratio 3:5 means 8 parts total. Green = 5/8 of 80% = 50%. 50% = 30 counters, so 100% = 60 counters.)
15% reduction (After first reduction: 600 × 0.90 = £540; Final price = £459; Second reduction from £540: (540 - 459)/540 × 100 = 81/540 × 100 = 15%)
30% passed both (The minimum overlap occurs when the sets are as separate as possible. 70% + 60% = 130%. The overlap is the extra 30% above 100%.)
£225 (Price after increase: 200 × 1.25 = £250; Price after loyalty discount: 250 × 0.90 = £225)
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