Mixture and Alligation: Mean Price

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Practice Questions

Concept Explanation

The mean price (average price per unit) of a mixture is the total cost divided by total quantity. It always lies between the two component prices.

Key Formulas

Mean price m = (C₁Q₁ + C₂Q₂) / (Q₁ + Q₂)
For n ingredients: m = Σ(C_iQ_i) / ΣQ_i
m is closer to the price of the ingredient taken in larger quantity

Example

5 kg at Rs. 12/kg and 15 kg at Rs. 20/kg. Mean = (60 + 300)/20 = Rs. 18/kg.

Common Trap

Mean price is a weighted average, not the midpoint of the two prices unless quantities are equal.

Q1 Easy

5 kg at Rs. 12/kg and 15 kg at Rs. 20/kg. Mean price is:
Q2 Easy

Mean of Rs. 10/kg and Rs. 30/kg with equal quantities is:
Q3 Medium

24 kg at Rs. 15/kg and 6 kg at Rs. 35/kg. Mean price is:
Q4 Medium

3 kg at Rs. 80/kg, 2 kg at Rs. 120/kg. Mean price is:
Q5 Easy

Mean price must lie between component prices. Rs. 25 and Rs. 45 give mean:
Q6 Medium

10 kg at Rs. 50/kg and 40 kg at Rs. 65/kg. Mean price is:
Q7 Easy

7 L at Rs. 6/L and 3 L at Rs. 16/L. Mean price is:

Q8 Hard

Mean of Rs. 18/kg and Rs. 42/kg is Rs. 30/kg. Ratio of quantities is:
Q9 Medium

18 kg at Rs. 22/kg and 12 kg at Rs. 28/kg. Mean price is:
Q10 Easy

1 kg at Rs. 100/kg and 9 kg at Rs. 60/kg. Mean price is:
Q11 Easy

Mean price of 2 kg at Rs. 45 and 3 kg at Rs. 60 is:
Q12 Medium

16 L at Rs. 5/L and 4 L at Rs. 25/L. Mean price is:
Q13 Hard

Which pair gives mean Rs. 26/kg?
Q14 Easy

Total 50 kg at mean Rs. 24/kg costs: