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(CiQi) / ΣQi
- 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.
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Q1 EasyThe cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2:3, then the price per kg of the mixed variety of rice is:ExplanationMean price = (C1Q1 + C2Q2)/(Q1 + Q2) = (2 × 15 + 3 × 20)/(2 + 3) = (30 + 60)/5 = 90/5 = Rs. 18 per kg. Hence the answer is Rs. 18.
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Q2 EasyA mixture of two varieties of rice costing Rs. 12 per kg and Rs. 18 per kg is made. If the mean price of the mixture is Rs. 15 per kg, then for every 1 kg of the first variety, how many kg of the second variety are taken?ExplanationMean price = Rs. 15. By alligation, quantity of Rs. 12 rice : quantity of Rs. 18 rice = (18 − 15) : (15 − 12) = 3 : 3 = 1 : 1. So for every 1 kg of the first variety, 1 kg of the second is taken. Hence the answer is 1 kg.
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Q3 Easy5 kg at Rs. 12/kg and 15 kg at Rs. 20/kg are mixed. The mean price per kg is:ExplanationMean price = (5 × 12 + 15 × 20)/(5 + 15) = (60 + 300)/20 = 360/20 = Rs. 18 per kg. Hence the answer is Rs. 18.
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Q4 EasyEqual quantities of tea at Rs. 10/kg and Rs. 30/kg are mixed. Mean price is:ExplanationFor equal quantities, mean price = (10 + 30)/2 = Rs. 20 per kg. Hence the answer is Rs. 20/kg.
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Q5 Easy3 kg at Rs. 80/kg and 2 kg at Rs. 120/kg give mean price:ExplanationMean = (3 × 80 + 2 × 120)/5 = (240 + 240)/5 = 480/5 = Rs. 96 per kg. Hence the answer is Rs. 96/kg.
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Q6 MediumTea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1:1:2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg is:ExplanationMean price = (sum of price × quantity parts) / total parts. Let the third variety cost Rs. x per kg. Then (1 × 126 + 1 × 135 + 2 × x)/4 = 153 ⇒ (261 + 2x)/4 = 153 ⇒ 261 + 2x = 612 ⇒ 2x = 351 ⇒ x = 175.50. Hence the price of the third variety is Rs. 175.50 per kg.
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Q7 MediumThree varieties of sugar costing Rs. 18/kg, Rs. 22/kg and Rs. 26/kg are mixed in the ratio 1:1:2. The mean price of the mixture per kg is:ExplanationMean price = (1 × 18 + 1 × 22 + 2 × 26)/(1 + 1 + 2) = (18 + 22 + 52)/4 = 92/4 = Rs. 23 per kg. Hence the answer is Rs. 23.
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Q8 MediumWheat at Rs. 30 per kg and Rs. 45 per kg are mixed in the ratio 2:1. The mean price of the mixture per kg is:ExplanationMean price = (2 × 30 + 1 × 45)/(2 + 1) = (60 + 45)/3 = 105/3 = Rs. 35 per kg. Hence the answer is Rs. 35.
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Q9 MediumA dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:ExplanationSelling the mixture at the cost price of pure milk with 25% gain means CP of mixture = (100/125) × CP of milk = (4/5) of milk CP. With free water, milk fraction in the mixture = 4/5, so water fraction = 1/5 = 20%. Hence water is 20% of the mixture.
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Q10 Medium24 kg at Rs. 15/kg and 6 kg at Rs. 35/kg are mixed. Mean price is:ExplanationMean = (24 × 15 + 6 × 35)/30 = (360 + 210)/30 = 570/30 = Rs. 19 per kg. Hence the answer is Rs. 19/kg.
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Q11 Medium10 kg at Rs. 50/kg and 40 kg at Rs. 65/kg. Mean price is:ExplanationMean = (10 × 50 + 40 × 65)/50 = (500 + 2600)/50 = 3100/50 = Rs. 62 per kg. Hence the answer is Rs. 62/kg.
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Q12 Medium18 kg at Rs. 22/kg and 12 kg at Rs. 28/kg. Mean price is:ExplanationMean = (18 × 22 + 12 × 28)/30 = (396 + 336)/30 = 732/30 = Rs. 24.4 per kg. Hence the answer is Rs. 24.4/kg.
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Q13 HardMean of Rs. 18/kg and Rs. 42/kg is Rs. 30/kg. The ratio of quantities is:ExplanationBy alligation, Q1 : Q2 = (42 − 30) : (30 − 18) = 12 : 12 = 1 : 1. Hence the quantities are in the ratio 1 : 1.
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Q14 HardWhich mix gives mean price Rs. 26/kg?ExplanationOption A: (200 + 300)/20 = Rs. 25. Option B: (20 × 22 + 10 × 34)/30 = (440 + 340)/30 = 780/30 = Rs. 26. Option C: (90 + 420)/20 = Rs. 25.5. Option D: (192 + 312)/20 = Rs. 25.2. Only B gives Rs. 26/kg. Hence the answer is B.
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DS1 Easy
What is the mean price per kg?
Statement IType 1 rice at Rs. 15/kg and Type 2 rice at Rs. 20/kg are mixed in the ratio 2:3.
Statement IITotal cost of 5 kg of the mixture is Rs. 90.
ExplanationStatement I: mean = (30 + 60)/5 = Rs. 18. Statement II: mean = 90/5 = Rs. 18. Either alone is sufficient. Answer: D. -
DS2 Easy
For the mean price of a two-ingredient mix. What is the mean price?
Statement I5 kg at Rs. 12/kg and 15 kg at Rs. 20/kg are mixed.
Statement IITotal 20 kg costs Rs. 360.
ExplanationStatement I: mean = 360/20 = Rs. 18. Statement II: mean = 360/20 = Rs. 18. Either alone is sufficient. Answer: D.
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DS3 Medium
What is the price of the third variety per kg?
Statement ITeas at Rs. 126/kg and Rs. 135/kg are mixed with a third variety in the ratio 1:1:2 and the mixture is worth Rs. 153/kg.
Statement IIOnly the mixture mean price is Rs. 153/kg.
ExplanationStatement I alone: (126 + 135 + 2x)/4 = 153 ⇒ x = 175.50. Statement II alone is insufficient. Answer: A. -
DS4 Medium
An HR analytics quiz asks whether the mean price of a rice mix is Rs. 18 per kg. Is the mean price Rs. 18/kg?
Statement IType 1 rice at Rs. 15/kg and Type 2 rice at Rs. 20/kg are mixed in the ratio 2:3.
Statement IIOnly the total cost of some mixture is Rs. 90 (quantities unknown).
ExplanationStatement I: mean = (2 × 15 + 3 × 20)/5 = 90/5 = Rs. 18, so the answer is Yes. Statement II alone cannot find mean price without quantity. Answer: A.