Numerical aptitude · Ratios and averages
Mixtures and alligation, made easy
💡 The idea
When two things are mixed, the mix lands between them. The closer it is to one, the more of that one is in it.
Cheap $4Dear $10Mix $610 − 6 = 46 − 4 = 2
🧭 The method: 3 steps
- Write the cheap and dear values, and the mix in the middle.
- Cross: dear − mix = parts of cheap, mix − cheap = parts of dear.
- Simplify the ratio.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. Rice at $4/kg and $10/kg is mixed to make $6/kg. Ratio?
- Dear − mix = 10 − 6 = 4 (cheap)
- Mix − cheap = 6 − 4 = 2 (dear)
- Cheap : dear = 4 : 2 = 2 : 1
Example 2. A 20 L can is milk : water = 3 : 1. Add 5 L water. New ratio?
- Milk = ¾ × 20 = 15 L, water = 5 L
- Add water: water = 10 L
- Milk : water = 15 : 10 = 3 : 2
Example 3. 40 L of juice: take out 4 L and add water, twice. Juice left?
- Each time juice × (1 − 4/40) = × 0.9
- 40 × 0.9 = 36
- 36 × 0.9 = 32.4 L
⚠️ Where people go wrong
- The bigger share belongs to the one closer to the mix.
- Change ratios into litres before adding water.
- In replacement, the second time you take out some water too.
📌 Remember
- Cheap : dear = (dear − mix) : (mix − cheap)