Elite Mathematics / Linear / Topics / Percentages IGCSE · 4MA1 · Topic Percentages: past paper questions & worked solutions
Every Percentages question from the 4MA1 papers in our bank, 2020–2026, sorted from easiest to hardest. Try each one first, then open the worked solution.
44 questions
186 marks in total
63% of papers (34 of 54) include it
0/26/18 easy / medium / hard
Questions, easiest first Level is estimated from marks: 1–2 easy, 3–4 medium, 5+ hard.
1. Jun 2026 P2H · Q4 Medium 3 marksShow worked solution Solution | Step 1 \[\text{Increase}=612-450=162.\]
Find the change from the original number.
Solution | Step 2 \[\text{Percentage increase}=\frac{162}{450}\times100=36\%.\]
Express the increase as a percentage of the July value, not the August value.
2. Jun 2026 P2H · Q8 Medium 3 marksShow worked solution Solution | Step 1 Let the original membership cost be \(C\) zloty. After a \(17\%\) increase, \(1.17C=3276\).
The new value is 117% of the original.
Solution | Step 2 \[C=\frac{3276}{1.17}=2800\text{ zloty}.\]
Divide by the increase multiplier.
Final answer \(2800\text{ zloty}\)
3. Jun 2026 P2HR · Q8 Medium 3 marksShow worked solution Solution | Step 1 Let the old salary be \(s\) euros. Then \[1.04s=36400.\]
The increased salary is 104% of the original.
Solution | Step 2 \[s=\frac{36400}{1.04}=35000.\]
Divide by the percentage multiplier.
Final answer \(35000\text{ euros}\).
4. Nov 2025 P1H · Q9 Medium 3 marksShow worked solution Tuesday s score was more Tuesday's score was \(12\%\) more than Monday's score, so Tuesday was \(112\%\) of Monday.
\[
1.12\times \text{Monday}=140
\]
\[
\text{Monday}=\frac{140}{1.12}=125
\]
Final answer \(125\) points
5. Jun 2025 P1H · Q5 Medium 3 marksShow worked solution The watch is reduced by The watch is reduced by \(28\%\), so the sale price is
\[
100\%-28\%=72\%
\]
of the normal price of the normal price.
\[
0.72\times \text{normal price}=198
\]
\[
\text{normal price}=198\div 0.72=275
\]
Final answer \(275\) euros.
6. Jun 2025 P2HR · Q9 Medium 3 marksShow worked solution A reduction of means the A reduction of \(15\%\) means the sale price is \(85\%\) of the normal price.
\[
0.85\times \text{normal price}=612
\]
\[
\text{normal price}=\frac{612}{0.85}=720
\]
Final answer \(720\) Swiss francs
7. May 2025 4WM2H · Q3 Medium 3 marksShow worked solution Convert standard form \[
\text{loss}=8000-5600=2400
\]
\[
\text{percentage loss}=\frac{2400}{8000}\times 100=30\%
\]
8. May 2025 4WM2HR · Q8 Medium 3 marksShow worked solution Required Sale price (after 15% reduction) = 612 Swiss francs. Find the normal price.
A 15% reduction means the A 15% reduction means the sale price is 85% of the normal price: 612 = 0.85 × Normal price
Solve for the normal price Solve for the normal price: $$\\text{Normal price} = \\frac{612}{0.85} = 720$$
Note Never calculate 15% of 612 and add it on — that gives 703.80 (wrong!). Always divide by the decimal multiplier.
Final answer Normal price = 720 Swiss francs
9. Jun 2024 P2HR · Q8 Medium 3 marksShow worked solution A reduction of means the A reduction of \(17\%\) means the sale price is \(83\%\) of the normal price.
\[
0.83\times \text{normal price}=6225
\]
\[
\text{normal price}=\frac{6225}{0.83}=7500
\]
Final answer \(7500\) rupees
10. May 2024 P1H · Q4 Medium 3 marksShow worked solution Calculate percentage April is \(15\%\) more than March, so April is \(115\%\) of March.
\[
1.15\times \text{March}=943
\]
\[
\text{March}=\frac{943}{1.15}=820
\]
Final answer \(820\) kilometres
11. Jun 2022 P2HR · Q8 Medium 3 marksShow worked solution Calculate percentage After a \(12\%\) increase, the ticket price is \(112\%\) of the original price.
\[
18.20=1.12\times \text{original price}
\]
\[
\text{original price}=\frac{18.20}{1.12}=16.25
\]
Final answer \(\pounds 16.25\)
12. Nov 2021 P2H · Q6 Medium 3 marksShow worked solution Total selling price Total selling price:
\[
12\times 2.45=29.40
\]
Profit Profit:
\[
29.40-21=8.40
\]
Percentage profit Percentage profit:
\[
\frac{8.40}{21}\times 100=40
\]
13. Nov 2021 P1H · Q8 Medium 3 marksShow worked solution Calculate percentage Sydney's population was \(22\%\) of Australia's total population.
\[
0.22\times \text{total}=5.48
\]
\[
\text{total}=\frac{5.48}{0.22}=24.909\ldots
\]
Calculate percentage Correct to 3 significant figures,
\[
24.909\ldots\approx 24.9
\]
Final answer \(24.9\) million
14. Jan 2021 P2HR · Q6 Medium 3 marksShow worked solution Wednesday s price was more Wednesday's price was \(5\%\) more than Monday's price.
Calculate percentage So
\[
1.26=1.05\times \text{Monday price}
\]
\[
\text{Monday price}=\frac{1.26}{1.05}=1.20
\]
The cost of litres on The cost of \(30\) litres on Monday was
\[
30\times 1.20=36
\]
Final answer \(\pounds 36\)
15. Jan 2021 P2H · Q10 Medium 3 marksShow worked solution The ratio of Team A The ratio of Team A to Team B is \(3:4\).
Use parts for Team A Use \(3\) parts for Team A and \(4\) parts for Team B.
Full time part from Team Full-time part from Team A:
\[
\frac45\times 3=\frac{12}{5}
\]
Full time part from Team Full-time part from Team B:
\[
24\%\times 4=\frac{24}{100}\times 4=\frac{24}{25}
\]
Total full time parts Total full-time parts:
\[
\frac{12}{5}+\frac{24}{25}
=\frac{60}{25}+\frac{24}{25}
=\frac{84}{25}
\]
Total parts Total parts:
\[
3+4=7
\]
Simplify fraction So the fraction who work full time is
\[
\frac{\frac{84}{25}}{7}=\frac{84}{175}=\frac{12}{25}
\]
Final answer \(\displaystyle \frac{12}{25}\)
16. Jan 2020 P1HR · Q7 Medium 3 marksShow worked solution The hat is reduced by The hat is reduced by \(15\%\), so the sale price is
\[
100\%-15\%=85\%
\]
of the normal price of the normal price.
\[
0.85 \times \text{normal price}=20.40
\]
\[
\text{normal price}=20.40\div 0.85=24
\]
Final answer \(24\) euros.
17. May-Nov 2020 P1H · Q9 Medium 3 marksShow worked solution A reduction of means the A reduction of \(20\%\) means the sale price is \(80\%\) of the normal price.
\[
0.80\times \text{normal price}=1080
\]
\[
\text{normal price}=\frac{1080}{0.80}=1350
\]
Final answer \(1350\) rupees
18. Jun 2026 P2HR · Q27 Medium 4 marksShow worked solution Solution | Step 1 \[\left(1+\frac{x}{100}\right)\left(1+\frac{2x}{100}\right)=1.3888.\]
The second increase acts on the already-increased house value.
Solution | Step 2 \[1+\frac{3x}{100}+\frac{2x^2}{10000}=1.3888\quad\Rightarrow\quad x^2+150x-1944=0.\]
Expand, subtract 1, and multiply by 5000.
Solution | Step 3 \[(x-12)(x+162)=0\quad\Rightarrow\quad x=12\text{ or }x=-162.\]
Factorize the quadratic.
Solution | Step 4 Reject \(x=-162\), since both changes are increases, so \(x>0\).
The positive root gives multipliers 1.12 and 1.24, whose product is 1.3888.
19. Nov 2025 4WM2H · Q4 Medium 4 marksShow worked solution Split the ratio Total parts = 6 + 7 + 3 = 16 parts
Evaluate fraction $$1 \\text{ part} = \\frac{960}{16} = 60 \\text{ trees}$$
Calculate value Cherry trees = 7 parts × 60 = 420 trees
Calculate percentage Morello trees = 0.65 × 420 = 273
Final answer 273
Always read carefully what the final question asks. A common mistake is stopping at the total number of cherry trees (420) instead of calculating the 65% morello portion.
20. Nov 2025 4WM2H · Q8 Medium 4 marksShow worked solution Calculate normal price **Step 1: Calculate Normal Price for Shop A.** A 25% discount means the sale price is 75% of the normal price. 0.75 × Normal<sub>*A*</sub> = 240 $$\\text{Normal}\_A = \\frac{240}{0.75} = 320 \\text{ euros}$$
Calculate normal price **Step 2: Calculate Normal Price for Shop B.** A discount of $\\frac{2}{9}$ means the sale price is $1 - \\frac{2}{9} = \\frac{7}{9}$ of the normal price. $$\\frac{7}{9} \\times \\text{Normal}\_B = 245$$ $$\\text{Normal}\_B = 245 \\times \\frac{9}{7} = 35 \\times 9 = 315 \\text{ euros}$$
Calculate value Difference = 320 − 315 = 5 euros
21. Nov 2024 P1H · Q7 Medium 4 marksShow worked solution Shop A discount Shop A discount:
\[
16\% \text{ of } 475=0.16\times 475=76
\]
Calculate percentage Shop B: \(408\) euros is \(85\%\) of the normal price.
\[
\text{normal price}=408\div 0.85=480
\]
Shop B discount Shop B discount:
\[
480-408=72
\]
Calculate percentage Since
\[
76>72
\]
Shop A gives the greater Shop A gives the greater discount.
Final answer Shop A gives the greater discount.
22. Nov 2023 P1H · Q3 Medium 4 marksShow worked solution Nina pays \[
1500+36(450)=1500+16200=17700
\]
Joshua s profit is Joshua's profit is
\[
17700-12500=5200
\]
Percentage profit Percentage profit:
\[
\frac{5200}{12500}\times 100=41.6
\]
23. Nov 2023 P1H · Q6 Medium 4 marksShow worked solution Calculate percentage Ticket A is sold for \(\frac{5}{6}\) of its normal price.
\[
\text{normal price of A}=140\times \frac{6}{5}=168
\]
Calculate percentage Ticket B has a \(20\%\) discount, so its sale price is \(80\%\) of the normal price.
\[
\text{normal price of B}=136\div 0.80=170
\]
The difference is \[
170-168=2
\]
Final answer The difference in normal prices is \(2\) euros.
24. May 2023 P1H · Q3 Medium 4 marksShow worked solution Number sold for 22 dirhams Number sold for 22 dirhams:
\[
70\%\times 60=42
\]
Number remaining Number remaining:
\[
60-42=18
\]
Total selling price Total selling price:
\[
42\times 22+18\times 19=924+342=1266
\]
Profit Profit:
\[
1266-780=486
\]
Percentage profit Percentage profit:
\[
\frac{486}{780}\times 100=62.307\ldots\%
\]
25. Jun 2022 P1HR · Q4 Medium 4 marksShow worked solution Total students Total students:
\[
180
\]
French French:
\[
15
\]
German German:
\[
45\%\times 180=81
\]
French or German French or German:
\[
15+81=96
\]
Italian or Spanish Italian or Spanish:
\[
180-96=84
\]
Convert standard form Write \(84\) as a percentage of \(96\):
\[
\frac{84}{96}\times 100=87.5
\]
26. May 2021 P2H · Q6 Medium 4 marksShow worked solution Split the ratio In each new bag, the ratio
\[
\text{nuts}:\text{seeds}=4:5
\]
has total parts has \(9\) total parts.
Weight of seeds in each Weight of seeds in each new bag:
\[
\frac{5}{9}\times 19.35=10.75\text{ kg}
\]
Decrease in seed weight Decrease in seed weight:
\[
12-10.75=1.25\text{ kg}
\]
Percentage decrease Percentage decrease:
\[
\frac{1.25}{12}\times 100=10.416\ldots\%
\]
27. Jun 2025 P2HR · Q4 Hard 5 marksShow worked solution Number of boxes of tiles Number of boxes of tiles:
\[
\frac{45}{1.5}=30
\]
Cost of tiles Cost of tiles:
\[
30\times 64=1920
\]
Cost of adhesive Cost of adhesive:
\[
5\times 12=60
\]
Total cost Total cost:
\[
1920+60=1980
\]
Profit Profit:
\[
3000-1980=1020
\]
Percentage profit Percentage profit:
\[
\frac{1020}{1980}\times 100=51.515\ldots\%
\]
28. May 2025 4WM2HR · Q5 Hard 5 marksShow worked solution Required Calculate Joshua’s percentage profit on the flooring job. Give answer to 1 d.p.
Number of boxes of tiles Number of boxes of tiles needed: $$\\frac{45\\,\\text{m}^2}{1.5\\,\\text{m}^2/\\text{box}} = 30 \\text{ boxes}$$
Cost of tiles 30 64 Cost of tiles: 30 × £64 = £1920
Cost of adhesive 5 12 Cost of adhesive: 5 × £12 = £60
Total cost (cost price) 1920 Total cost (cost price): £1920 + £60 = £1980
Profit and percentage profit Profit Profit and percentage profit: Profit = £3000 − £1980 = £1020 $$\\%\\,\\text{Profit} = \\frac{1020}{1980} \\times 100 = 51.515\\ldots\\%$$
Note Always divide profit by the **cost price** (£1980), not the selling price (£3000). Dividing by £3000 gives 34.0% — a common but wrong answer.
Final answer Percentage profit = 51.5%
29. Nov 2024 P2H · Q4 Hard 5 marksShow worked solution Calculate percentage For part (a),
\[
17\%\text{ of }N=357
\]
\[
0.17N=357
\]
\[
N=\frac{357}{0.17}=2100
\]
Calculate percentage For part (b), the increase in population is
\[
806-650=156
\]
Percentage increase Percentage increase:
\[
\frac{156}{650}\times 100=24
\]
Final answer (a) \(N=2100\), (b) \(24\%\)
30. Jun 2024 P2H · Q8 Hard 5 marksShow worked solution The ratio parts are \[
9+4+2=15
\]
\[
\text{tulips}=600\times \frac{9}{15}=360,\quad
\text{crocuses}=600\times \frac{4}{15}=160,\quad
\text{daffodils}=600\times \frac{2}{15}=80
\]
Yellow tulips Yellow tulips:
\[
45\%\times 360=0.45\times 360=162
\]
Yellow crocuses Yellow crocuses:
\[
\frac{5}{8}\times 160=100
\]
All the daffodil bulbs are All the daffodil bulbs are yellow, so
\[
162+100+80=342
\]
Final answer \(342\) bulbs
31. May 2024 P1HR · Q3 Hard 5 marksShow worked solution The ratio parts are \[
3+2=5
\]
White loaves White loaves:
\[
200\times \frac{3}{5}=120
\]
Brown loaves Brown loaves:
\[
200\times \frac{2}{5}=80
\]
Profit on each white loaf Profit on each white loaf:
\[
40\%\times 1.50=0.60
\]
Profit on each brown loaf Profit on each brown loaf:
\[
60\%\times 1.75=1.05
\]
Total profit Total profit:
\[
120\times 0.60+80\times 1.05=72+84=156
\]
Final answer \(156\) pounds
32. May 2024 P1H · Q14 Hard 5 marksShow worked solution Let Abel s savings be Let Abel's savings be \(A\).
Calculate percentage Bahira has \(45\%\) more than Abel, so
\[
B=1.45A
\]
Their combined savings are \[
A+1.45A=15435
\]
\[
2.45A=15435
\]
\[
A=6300
\]
Calculate percentage So
\[
B=1.45\times 6300=9135
\]
Bahira s savings are times Bahira's savings are \(\frac{3}{2}\) times Chanda's savings, so
\[
9135=\frac{3}{2}C
\]
\[
C=9135\times \frac{2}{3}=6090
\]
Final answer \(6090\) dinars
33. Jun 2022 P2H · Q8 Hard 5 marksShow worked solution The ratio has parts The ratio \(7:5:3\) has \(15\) parts.
Birthday cards Birthday cards:
\[
\frac7{15}\times 300=140
\]
Anniversary cards Anniversary cards:
\[
\frac5{15}\times 300=100
\]
Congratulations cards Congratulations cards:
\[
\frac3{15}\times 300=60
\]
Birthday cards with numbers Birthday cards with numbers:
\[
\frac25\times 140=56
\]
Anniversary cards with numbers Anniversary cards with numbers:
\[
36\%\times 100=36
\]
Congratulations cards with numbers Congratulations cards with numbers:
\[
0
\]
Total with numbers Total with numbers:
\[
56+36=92
\]
Fraction of all cards Fraction of all cards:
\[
\frac{92}{300}=\frac{23}{75}
\]
Final answer \(\displaystyle \frac{23}{75}\)
34. Jun 2022 P1H · Q13 Hard 5 marksShow worked solution Payment 1 is \[
\frac38
\]
Payment 2 is \[
45\%=\frac{45}{100}=\frac9{20}
\]
Together Together:
\[
\frac38+\frac9{20}
=\frac{15}{40}+\frac{18}{40}
=\frac{33}{40}
\]
Calculate percentage So Payment 3 is
\[
1-\frac{33}{40}=\frac7{40}
\]
Calculate percentage Payment 3 is \(\$406\), so
\[
\frac7{40}\times \text{total}=406
\]
\[
\text{total}=406\times \frac{40}{7}=2320
\]
Payment 2 is \[
45\%\times 2320=1044
\]
35. Jan 2022 P1H · Q4 Hard 5 marksShow worked solution Small mugs Small mugs:
\[
\frac25\times 150=60
\]
Medium mugs Medium mugs:
\[
32\%\times 150=48
\]
Large mugs Large mugs:
\[
150-60-48=42
\]
Revenue Revenue:
\[
60(8.50)+48(11.20)+42(14.20)
\]
\[
=510+537.60+596.40=1644
\]
Profit Profit:
\[
1644-1140=504
\]
Percentage profit Percentage profit:
\[
\frac{504}{1140}\times 100=44.21\ldots
\]
Correct to the nearest whole Correct to the nearest whole number:
\[
44\%
\]
36. Jan 2022 P2H · Q8 Hard 5 marksShow worked solution Increase from 2018 to 2019 Increase from 2018 to 2019:
\[
231776-228314=3462
\]
Percentage increase Percentage increase:
\[
\frac{3462}{228314}\times 100=1.516\ldots
\]
Correct to one decimal place Correct to one decimal place:
\[
1.5\%
\]
Calculate percentage For part (b), the 2019 price was \(7.7\%\) greater than the 2017 price.
\[
231776=1.077\times \text{2017 price}
\]
\[
\text{2017 price}=\frac{231776}{1.077}=215205.19\ldots
\]
Correct to 3 significant figures Correct to 3 significant figures:
\[
215000
\]
Final answer (a) \(1.5\%\), (b) \(\pounds 215000\)
37. May-Nov 2020 P1HR · Q10 Hard 5 marksShow worked solution The ratio parts are \[
3+2+5=10
\]
Numbers of cakes made Numbers of cakes made:
\[
\text{chocolate}=80\times\frac{3}{10}=24
\]
\[
\text{lemon}=80\times\frac{2}{10}=16
\]
\[
\text{fruit}=80\times\frac{5}{10}=40
\]
Cakes sold Cakes sold:
\[
\text{chocolate}=24,\quad \text{lemon}=\frac{3}{4}\times 16=12,\quad \text{fruit}=\frac{7}{8}\times 40=35
\]
Total profit Total profit:
\[
24(2.00)+12(1.70)+35(2.40)=48+20.40+84=152.40
\]
Final answer \(152.40\) pounds
38. Specimen 4WM2H · Q12 Hard 5 marksShow worked solution Calculate percentage \[
\frac25=40\%
\]
Calculate percentage So Payments 1 and 2 together are
\[
40\%+45\%=85\%
\]
This means Payment 3 is \[
100\%-85\%=15\%
\]
Calculate percentage So
\[
15\%=405
\]
\[
1\%=27
\]
Payment 2 is Payment 2 is \(45\%\):
\[
45\times 27=1215
\]
39. Jun 2025 P1H · Q2 Hard 6 marksShow worked solution Number of cups Number of cups:
\[
80\times 4=320
\]
Cost to make the cups Cost to make the cups:
\[
320\times 6=1920
\]
Profit Profit:
\[
2160-1920=240
\]
Percentage profit Percentage profit:
\[
\frac{240}{1920}\times 100=12.5
\]
Find lower bound The height \(9\) cm correct to the nearest cm has lower bound
\[
8.5\text{ cm}
\]
Find upper bound The weight \(120\) g correct to the nearest \(10\) g has upper bound
\[
125\text{ g}
\]
Final answer (a) \(12.5\%\), (b) \(8.5\) cm, (c) \(125\) g
40. Jan 2021 P2H · Q3 Hard 6 marksShow worked solution Profit Profit:
\[
520-465=55
\]
Percentage profit Percentage profit:
\[
\frac{55}{465}\times 100=11.827\ldots
\]
Correct to 3 significant figures Correct to 3 significant figures:
\[
11.8\%
\]
Calculate statistic For the sale price, a \(12\%\) decrease means \(88\%\) of the original price:
\[
550\times 0.88=484
\]
Final answer (a) \(11.8\%\), (b) \(\$484\)
41. May-Nov 2020 P1HR · Q5 Hard 6 marksShow worked solution The population increase is \[
8265-7500=765
\]
Percentage increase Percentage increase:
\[
\frac{765}{7500}\times 100=10.2\%
\]
The T shirt sale price The T-shirt sale price is after a \(30\%\) reduction, so it is \(70\%\) of the normal price.
\[
0.70\times \text{normal price}=31.50
\]
\[
\text{normal price}=31.50\div 0.70=45
\]
Final answer (a) \(10.2\%\), (b) \(45\) euros.
42. Jun 2023 P2HR · Q6 Hard 7 marksShow worked solution Pierre s old weekly pay Pierre's old weekly pay is \(400\) euros.
His new weekly pay is \[
14\times 7\times 5=490
\]
The increase is \[
490-400=90
\]
Percentage increase Percentage increase:
\[
\frac{90}{400}\times 100=22.5\%
\]
Marie s new salary is Marie's new salary is after a \(6\%\) decrease, so it is \(94\%\) of her old salary.
\[
0.94\times \text{old salary}=23030
\]
\[
\text{old salary}=23030\div 0.94=24500
\]
Final answer Pierre's pay increased by \(22.5\%\). Marie's old salary was \(24500\) euros.
43. Jan 2022 P2HR · Q2 Hard 7 marksShow worked solution Mary saved in 2021 Mary saved in 2021:
\[
78\times 12=936
\]
Increase from 2020 Increase from 2020:
\[
936-720=216
\]
Percentage increase Percentage increase:
\[
\frac{216}{720}\times 100=30
\]
Calculate percentage So \(P=30\).
Coupon A saves \[
18\%\times 1600=0.18\times 1600=288
\]
Coupon B saves of the Coupon B saves \(12.5\%\) of the accommodation and flights together:
\[
1600+800=2400
\]
\[
12.5\%\times 2400=0.125\times 2400=300
\]
Coupon B saves more money Coupon B saves more money.
Final answer (a) \(P=30\), (b) Coupon B
44. Jan 2020 P2H · Q8 Hard 7 marksShow worked solution Convert standard form From 2016 to 2017, the increase is
\[
545-500=45
\]
\[
\frac{45}{500}\times 100=9\%
\]
Convert standard form From 2017 to 2018, the increase is
\[
592-545=47
\]
\[
\frac{47}{545}\times 100\approx 8.62\%
\]
Calculate percentage So Brigitte is not correct because the second percentage increase is smaller.
Calculate percentage For Henri, \(952\) is \(85\%\) of the original price because there is a \(15\%\) discount.
\[
\text{original price}=952\div 0.85=1120
\]
The discount is \[
1120-952=168
\]
Final answer Brigitte is not correct; the discount is \(168\) euros.
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