Practice Questions
Concept Explanation
Most mixture questions involve exactly two items at different rates. Find either the mean price, a missing quantity, or the mixing ratio.
Key Formulas
- Mean m = (C1Q1 + C2Q2) / (Q1 + Q2)
- Q2 = Q1(C1 − m) / (m − C2) from alligation
- Total cost = C1Q1 + C2Q2
Example
Mix 8 kg at Rs. 25/kg with 12 kg at Rs. 40/kg. Mean = (200 + 480)/20 = Rs. 34/kg.
Common Trap
When finding a missing quantity, set up the weighted mean equation rather than guessing.
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Q1 Easy
8 kg at Rs. 25/kg and 12 kg at Rs. 40/kg. Mean price is:
ExplanationMean = (200 + 480)/20 = Rs. 34/kg. -
Q2 Medium
How many kg at Rs. 60/kg mix with 20 kg at Rs. 40/kg for Rs. 50/kg?
Explanation(800 + 60x)/(20 + x) = 50 gives 10x = 200, so x = 20 kg. -
Q3 Easy
6 L at Rs. 12/L and 14 L at Rs. 22/L. Mean price is:
ExplanationMean = (72 + 308)/20 = Rs. 19/L. -
Q4 Easy
25 kg at Rs. 32/kg and 15 kg at Rs. 48/kg. Total cost is:
ExplanationTotal = 800 + 720 = Rs. 1520. -
Q5 Medium
Rs. 35/kg and Rs. 55/kg mixed for Rs. 43/kg. Ratio is:
Explanation(55 − 43) : (43 − 35) = 12 : 8 = 3 : 2. -
Q6 Hard
10 kg at Rs. 70/kg and x kg at Rs. 100/kg give Rs. 85/kg. Find x.
Explanation(700 + 100x)/(10 + x) = 85 gives 15x = 150, x = 10 kg. -
Q7 Medium
40 kg at Rs. 16/kg and 10 kg at Rs. 36/kg. Mean price is:
ExplanationMean = (640 + 360)/50 = Rs. 20/kg.
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Q8 Medium
Two items at Rs. 18/kg and Rs. 42/kg in ratio 3 : 1. Mean price is:
ExplanationMean = (3×18 + 1×42)/4 = 96/4 = Rs. 24/kg. -
Q9 Easy
30 L at Rs. 8/L and 20 L at Rs. 18/L. Mean price is:
ExplanationMean = (240 + 360)/50 = Rs. 12/L. -
Q10 Hard
Cost of 35 kg mix at Rs. 44/kg from 20 kg at Rs. 38/kg and rest at Rs. x/kg. Find x.
Explanation1540 = 760 + 15x gives 15x = 780, x = Rs. 52/kg. -
Q11 Easy
5 kg at Rs. 90/kg and 15 kg at Rs. 30/kg. Mean price is:
ExplanationMean = (450 + 450)/20 = Rs. 45/kg. -
Q12 Hard
Rs. 28/kg and Rs. 52/kg for Rs. 40/kg. Cheaper quantity in 40 kg mix is:
ExplanationRatio = (52 − 40) : (40 − 28) = 1 : 1. Cheaper = 20 kg. -
Q13 Medium
14 kg at Rs. 55/kg and 6 kg at Rs. 85/kg. Mean price is:
ExplanationMean = (770 + 510)/20 = Rs. 64/kg. -
Q14 Hard
Which gives mean Rs. 36/kg?
ExplanationOption D: (120 + 600)/20 = Rs. 36/kg.
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DS1 Easy
What is the mean price?
Statement I8 kg at Rs. 25/kg and 12 kg at Rs. 40/kg are mixed.
Statement IITotal 20 kg costs Rs. 680.
ExplanationEach gives mean = 680/20 = Rs. 34/kg. -
DS2 Medium
How many kg of the dearer item are needed?
Statement I20 kg at Rs. 40/kg is mixed with dearer at Rs. 60/kg for Rs. 50/kg.
Statement IIMean price is Rs. 50/kg.
ExplanationStatement I alone: x = 20 kg from (800+60x)/(20+x)=50.
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DS3 Medium
Is total cost Rs. 1520?
Statement I25 kg at Rs. 32/kg and 15 kg at Rs. 48/kg are mixed.
Statement IIMean price is Rs. 38/kg and total is 40 kg.
ExplanationEach gives total = 800 + 720 = Rs. 1520. -
DS4 Easy
What is the mixing ratio?
Statement IItems at Rs. 35/kg and Rs. 55/kg give mean Rs. 43/kg.
Statement IICheaper and dearer are mixed 3 : 2.
ExplanationEach gives ratio 3 : 2.