Average, Mixture & Alligation • Topic 2 of 4

Weighted Average

When groups of different sizes combine, the overall average is the weighted average: (n1 a1 + n2 a2) / (n1 + n2). This is the engine behind average marks of two sections, average price of mixed stock, and average speed when times differ. Do not average the averages unless the group sizes are equal.

✅ Solved examples

1. Section A (40 students) averages 60; section B (60 students) averages 70. Combined average?
(40x60 + 60x70)/100 = (2400 + 4200)/100 = 66.
2. 20 kg of rice at 30/kg mixed with 30 kg at 40/kg. Average price?
(20x30 + 30x40)/50 = (600 + 1200)/50 = 36.
3. A man drives 2 hours at 40 km/h and 3 hours at 60 km/h. Average speed?
Distance = 80 + 180 = 260 km; time 5 h; avg = 52 km/h.
4. Two classes: 25 students avg 16 years and 15 students avg 20 years. Combined average age?
(25x16 + 15x20)/40 = (400 + 300)/40 = 17.5 years.

✏️ Practice — try these, take hints as needed

1. 30 boys avg 50, 20 girls avg 60. Combined?
(30x50 + 20x60)/50.
(1500+1200)/50.
—
54
2. 10 kg at 20 + 15 kg at 30. Avg price?
(200+450)/25.
650/25.
—
26
3. Travel 3 h at 50 and 2 h at 75. Avg speed?
Distance 150+150 = 300.
Time 5.
—
60 km/h
4. 12 men avg 30, 8 men avg 40. Combined?
(360+320)/20.
680/20.
—
34
5. 40% scored 90, 60% scored 40. Average?
0.4x90 + 0.6x40.
36 + 24.
—
60

📝 Topic test — 8 questions

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