Practice Questions
Concept Explanation
A mixture combines two or more ingredients at different rates. The average (mean) rate of the final mix depends on the quantities and their individual prices or values.
Key Formulas
- Mean price = (C1 × Q1 + C2 × Q2) / (Q1 + Q2)
- Total cost = Sum of (quantity × rate) for each ingredient
- Total quantity = Q1 + Q2 + …
Example
Mix 10 kg at Rs. 30/kg with 10 kg at Rs. 50/kg. Total cost = 300 + 500 = Rs. 600 for 20 kg. Mean price = 600/20 = Rs. 40/kg.
Common Trap
Do not take a simple average of prices unless quantities are equal. Weight by quantity always.
-
Q1 Easy
10 kg at Rs. 30/kg mixed with 10 kg at Rs. 50/kg gives mean price:
ExplanationEqual quantities: mean = (30 + 50)/2 = Rs. 40/kg. -
Q2 Easy
20 L at Rs. 5/L and 30 L at Rs. 8/L. Mean price per litre is:
ExplanationMean = (100 + 240)/50 = Rs. 6.8/L. -
Q3 Easy
60 kg rice at Rs. 20/kg mixed with 40 kg at Rs. 30/kg. Mean price is:
ExplanationMean = (1200 + 1200)/100 = Rs. 24/kg. -
Q4 Medium
15 L oil at Rs. 80/L and 5 L at Rs. 120/L. Mean price is:
ExplanationMean = (1200 + 600)/20 = Rs. 90/L. -
Q5 Easy
3 kg sugar at Rs. 40/kg and 2 kg at Rs. 55/kg. Mean price is:
ExplanationMean = (120 + 110)/5 = Rs. 46/kg. -
Q6 Medium
25 kg mixture at Rs. 32/kg is made from 15 kg at Rs. 28/kg and the rest at Rs. x/kg. Find x.
Explanation800 = 420 + 10x, so 10x = 380 and x = Rs. 38/kg. -
Q7 Medium
12 L at Rs. 4/L and 8 L at Rs. 7/L. Mean price is:
ExplanationMean = (48 + 56)/20 = Rs. 5.2/L.
-
Q8 Easy
50 kg wheat at Rs. 18/kg and 50 kg at Rs. 22/kg. Mean price is:
ExplanationEqual weights: mean = (18 + 22)/2 = Rs. 20/kg. -
Q9 Hard
How many kg at Rs. 50/kg must mix with 10 kg at Rs. 30/kg to get Rs. 38/kg?
Explanation(300 + 50x)/(10 + x) = 38 gives 12x = 80, so x = 6.67 kg. -
Q10 Easy
4 kg at Rs. 60/kg and 6 kg at Rs. 90/kg. Mean price is:
ExplanationMean = (240 + 540)/10 = Rs. 78/kg. -
Q11 Easy
40 L at Rs. 10/L and 60 L at Rs. 15/L. Mean price is:
ExplanationMean = (400 + 900)/100 = Rs. 13/L. -
Q12 Easy
8 kg at Rs. 45/kg and 12 kg at Rs. 60/kg. Mean price is:
ExplanationMean = (360 + 720)/20 = Rs. 54/kg. -
Q13 Easy
Total cost of 30 kg mixture at Rs. 25/kg is:
ExplanationTotal cost = 30 × 25 = Rs. 750. -
Q14 Hard
Which mix gives mean Rs. 35/kg?
ExplanationOption A: (600 + 800)/40 = Rs. 35/kg.
-
DS1 Easy
What is the mean price per kg?
Statement I20 kg at Rs. 30/kg is mixed with 20 kg at Rs. 40/kg.
Statement IITotal 40 kg costs Rs. 1400.
ExplanationEach gives mean = 1400/40 = Rs. 35/kg. -
DS2 Easy
What is the total quantity of the mixture?
Statement ITwo ingredients are mixed in a vessel.
Statement IIThe weights are 15 kg and 25 kg.
ExplanationStatement II alone gives total = 15 + 25 = 40 kg.
-
DS3 Medium
Is the mean price greater than Rs. 50/kg?
Statement IEqual quantities at Rs. 40/kg and Rs. 60/kg are mixed.
Statement IIEqual quantities at Rs. 45/kg and Rs. 55/kg are mixed.
ExplanationI gives Rs. 50/kg; II gives Rs. 50/kg. Neither shows mean above Rs. 50/kg. -
DS4 Easy
What is the total cost of the mixture?
Statement I10 kg is taken at Rs. 25/kg.
Statement II15 kg is taken at Rs. 35/kg.
ExplanationNeed both: total cost = 250 + 525 = Rs. 775.