GCSE ratio questions go well beyond simple sharing. You may need to combine two separate ratios into a three-part ratio, set up equations from ratio information, or find a missing quantity when only one part is given. Mastering a few key techniques handles the full range of GCSE problem types.
How do you find a missing quantity given one share?
If you know one person's share and the ratio, you can find one "part" and scale everything from there.
Example: Aisha and Ben share money in the ratio 4 : 7. Aisha receives £36. How much does Ben receive, and what was the total?
- Aisha's share = 4 parts = £36, so one part = £36 ÷ 4 = £9.
- Ben's share = 7 × £9 = £63.
- Total = £36 + £63 = £99 (or 11 × £9 = £99). ✓
How do you find an original total when given the difference?
Example: Carla and Dan share sweets in the ratio 3 : 8. Dan receives 25 more sweets than Carla. How many sweets are there in total?
- Difference in parts: 8 − 3 = 5 parts.
- 5 parts = 25 sweets, so one part = 5 sweets.
- Total parts = 3 + 8 = 11, so total sweets = 11 × 5 = 55 sweets. ✓
Check: Carla = 3 × 5 = 15; Dan = 8 × 5 = 40; difference = 25 ✓; total = 55 ✓.
How do you combine two ratios into a three-part ratio?
When A : B = p : q and B : C = r : s, make the B values equal by scaling each ratio so B is the same number in both.
Example 1 — B is already the same: A : B = 2 : 3 and B : C = 3 : 5. B is 3 in both ratios, so A : B : C = 2 : 3 : 5 directly.
Example 2 — B values differ: A : B = 2 : 3 and B : C = 4 : 5.
| Ratio | Scale factor | New ratio |
|---|---|---|
| A : B = 2 : 3 | ×4 | A : B = 8 : 12 |
| B : C = 4 : 5 | ×3 | B : C = 12 : 15 |
B is now 12 in both. So A : B : C = 8 : 12 : 15.
Always scale so that the shared term (B here) has the same value in both ratios — use the LCM of the two B values.
How do you solve ratio problems using algebra?
When a ratio question involves an unknown, let the parts of the ratio be multiples of a variable.
Example: Two numbers are in the ratio 5 : 3. Their sum is 56. Find both numbers.
Let the numbers be 5k and 3k.
5k + 3k = 568k = 56k = 7
The numbers are 5 × 7 = 35 and 3 × 7 = 21. Check: 35 : 21 = 5 : 3 ✓; 35 + 21 = 56 ✓.
This method works for any number of parts: let each part equal (ratio part) × k, write your equation, solve for k.
How do you handle ratios that change?
Some GCSE questions describe a ratio that changes — for example, when a quantity is added to one part.
Example: Orange and blackcurrant squash are mixed in the ratio 1 : 4. 6 more litres of orange are added, making the ratio 1 : 2. How many litres of blackcurrant are there?
Let original amount of orange = x litres. Then blackcurrant = 4x litres.
After adding 6 litres of orange: new ratio is (x + 6) : 4x = 1 : 2.
Cross-multiply: 2(x + 6) = 1 × 4x
2x + 12 = 4x
12 = 2x
x = 6
Blackcurrant = 4 × 6 = 24 litres. ✓
Check: orange after = 6 + 6 = 12; ratio 12 : 24 = 1 : 2 ✓.
What real-life contexts appear in GCSE ratio questions?
- Recipes and mixtures: Scaling ingredients up or down while keeping the ratio constant.
- Currency exchange: Sharing in a given ratio or finding how much one currency buys.
- Maps and scale: A map scale is a ratio (e.g. 1 : 50 000). Finding real distances from map distances.
- Mixing paints or chemicals: Combining in a given ratio by volume or mass.
- Financial splits: Profit sharing between business partners in an agreed ratio.
Frequently asked questions
What is the difference between a ratio and a fraction?
A ratio compares part to part (e.g. 2 : 3 means for every 2 of one thing there are 3 of another). A fraction compares part to whole (e.g. 2/5 means 2 out of every 5 total). They are related: in a 2 : 3 ratio, the first quantity is 2/5 of the total.
How do you simplify a ratio before solving a harder problem?
Divide all parts of the ratio by their HCF. For example, 12 : 18 simplifies to 2 : 3 (dividing by 6). Always simplify at the start — it reduces arithmetic errors in multi-step problems.
Can a ratio have three or more parts?
Yes. A three-part ratio such as 2 : 3 : 5 means three quantities are in those relative amounts. The total number of parts is 2 + 3 + 5 = 10, and each quantity is its part multiplied by (total ÷ 10). The same method scales to any number of parts.
How do I know if a ratio problem requires algebra?
If the question gives information about a relationship between shares (their sum, their difference, or what happens when something is added) rather than the actual value of one share, set up an equation using k or x for one part. If you are told directly that one share equals a specific amount, simply divide to find one part and scale.
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