Free Ratio & proportion questions for IGCSE Mathematics (0580), part of Number. Each question has the answer and the marking points an examiner would look for.
Generate a full Ratio & Proportion worksheet →All Number questionsIn a club, the ratio boys : girls = 5 : 2.
8 boys leave the club and 22 girls join the club.
There are now the same number of boys and girls.
Find how many members the club had at the start.
| Part | Answer and marking points | Marks |
|---|---|---|
| 70 5k − 8 = 2k + 22 (or equivalent) M2 k = 10 A1 70 A1 | 4 |
Alloy A contains copper and zinc in the ratio 3 : 2 by mass.
Alloy B contains copper, zinc and tin in the ratio 5 : 3 : 2 by mass.
a kg of alloy A and b kg of alloy B are melted together. In the mixture, the ratio copper : zinc is 13 : 8.
Find a : b in its simplest form and the percentage of the mixture that is tin.
A different mixture of alloys A and B has copper : zinc between 8 : 5 and 13 : 8.
Find the range of possible values of the percentage of the mixture that is tin.
Pure copper is added to 10 kg of the mixture from part (a) so that the ratio copper : zinc becomes 2 : 1.
Find the mass of copper added, and the ratio copper : zinc : tin in the final alloy in its simplest form.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | a : b = 1 : 4; 16% copper 0.6a + 0.5b, zinc 0.4a + 0.3b B1 8(0.6a + 0.5b) = 13(0.4a + 0.3b) M1 0.1b = 0.4a, a : b = 1 : 4 A1 tin = 0.2b = 0.8a out of 5a M1 16% A1 | 5 |
| (b) | 1313% to 16% 8(0.4a + 0.3b) = 5(0.6a + 0.5b) gives b = 2a M1 tin = 0.4a3a = 1313% A1 the copper : zinc ratio and the tin percentage both increase as the proportion of B increases M1 between 1313% and 16% A1 | 4 |
| (c) | 1.2 kg; 32 : 16 : 8 → 4 : 2 : 1 10 kg contains copper 5.2 kg, zinc 3.2 kg, tin 1.6 kg B1 5.2 + c = 2 × 3.2 M1 c = 1.2 kg A1 6.4 : 3.2 : 1.6 = 4 : 2 : 1 B1 | 4 |
Share $220 in the ratio 4 : 3 : 4.
In a club the ratio of boys to girls is 3 : 6. There are 9 more girls than boys. Work out the total number of members.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | $80 : $60 : $80 220 ÷ 11 = 20 M1 All three correct A1 | 2 |
| (b) | 27 9 ÷ 3 = 3 M1 27 A1 | 2 |
Amir, Bella and Chen share some money.
The ratio Amir’s share : Bella’s share = 2 : 5.
The ratio Bella’s share : Chen’s share = 4 : 3.
Chen receives $245 more than Amir.
Calculate the total amount of money they share.
| Part | Answer and marking points | Marks |
|---|---|---|
| $1505 A : B : C = 8 : 20 : 15 M1 15 − 8 = 7 parts = $245 M1 1 part = $35 M1 1505 A1 | 4 |
In a club, the ratio boys : girls = 7 : 4.
7 boys leave the club and 29 girls join the club.
There are now the same number of boys and girls.
Find how many members the club had at the start.
| Part | Answer and marking points | Marks |
|---|---|---|
| 132 7k − 7 = 4k + 29 (or equivalent) M2 k = 12 A1 132 A1 | 4 |
Share $420 in the ratio 1 : 3 : 2.
In a club the ratio of boys to girls is 2 : 4. There are 18 more girls than boys. Work out the total number of members.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | $70 : $210 : $140 420 ÷ 6 = 70 M1 All three correct A1 | 2 |
| (b) | 54 18 ÷ 2 = 9 M1 54 A1 | 2 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in