Average, Mixture & Alligation • Topic 3 of 4

Alligation Rule

Alligation gives the ratio in which two things at known values mix to hit a mean value: cheaper : dearer = (dearer - mean) : (mean - cheaper). Picture the cross: write the two values at the top corners, the mean in the middle, and take diagonal differences. It works for prices, concentrations, speeds and even average ages — any weighted average run backwards to find the mix ratio.

✅ Solved examples

1. In what ratio mix rice at 24/kg and 40/kg to get 30/kg?
cheaper:dearer = (40-30):(30-24) = 10:6 = 5:3.
2. How much water to add to 40 L of milk to make the average value drop from 20 to 16 per litre (water value 0)?
milk:water = (16-0):(20-16) = 16:4 = 4:1; for 40 L milk, water = 10 L.
3. Two alloys have 40% and 60% copper. Mix to get 45% copper — ratio?
(60-45):(45-40) = 15:5 = 3:1.
4. Tea at 80 and 100 mixed to sell at 90 (no profit). Ratio?
(100-90):(90-80) = 10:10 = 1:1.

✏️ Practice — try these, take hints as needed

1. Mix sugar 30 and 45 to get 35. Ratio?
(45-35):(35-30).
10:5.
—
2:1
2. Alloys 30% and 70% zinc to 40% zinc. Ratio?
(70-40):(40-30).
30:10.
—
3:1
3. Milk 18/L, water 0; want 15/L. Milk:water?
(15-0):(18-15).
15:3.
—
5:1
4. Rice 50 and 60 to get 54. Ratio?
(60-54):(54-50).
6:4.
—
3:2
5. Two speeds 40 and 60 for average 45. Time ratio?
(60-45):(45-40).
15:5.
—
3:1

📝 Topic test — 8 questions

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