Practice Questions
Concept Explanation
Milk and water problems are classic mixture questions. Milk is the valuable component; water is the filler. Use ratios or alligation to find quantities or concentrations.
Key Formulas
- Milk : water ratio defines concentration: milk fraction = milk/(milk + water)
- Adding water dilutes: new milk fraction = old milk / (old total + water added)
- Alligation applies when mixing two concentrations of milk
Example
Milk : water = 5 : 3 in 32 L. Milk = 5/8 × 32 = 20 L, water = 12 L.
Common Trap
When water is added, milk quantity stays the same; only total volume increases.
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Q1 Easy
Milk : water = 5 : 3 in 32 L. Milk is:
ExplanationMilk = 5/8 × 32 = 20 L. -
Q2 Easy
Milk : water = 7 : 3 in 50 L. Water is:
ExplanationWater = 3/10 × 50 = 15 L. -
Q3 Easy
20 L milk mixed with 5 L water. Milk percentage is:
ExplanationMilk = 20/25 = 80%. -
Q4 Easy
24 L at 75% milk. Milk quantity is:
ExplanationMilk = 0.75 × 24 = 18 L. -
Q5 Medium
18 L milk in a 30 L vessel. How much water to add for 60% milk?
Explanation18/30 = 60% already. No water needed. -
Q6 Easy
Milk : water = 4 : 1. Milk percentage is:
ExplanationMilk = 4/5 = 80%. -
Q7 Medium
60 L milk, 15 L water added. New milk percentage is:
ExplanationMilk = 60/75 = 80%.
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Q8 Hard
Mix 40 L (80% milk) with 10 L water. Milk percentage is:
ExplanationMilk = 32 L in 50 L = 64%. -
Q9 Easy
Ratio 3 : 2 milk : water in 50 L. Milk is:
ExplanationMilk = 3/5 × 50 = 30 L. -
Q10 Easy
12 L milk and 8 L water. Milk : water ratio is:
ExplanationRatio = 12 : 8 = 3 : 2. -
Q11 Medium
Pure milk 30 L, 6 L removed and 6 L water added. Milk left is:
ExplanationMilk left = 30 − 6 = 24 L. -
Q12 Medium
80% milk solution: 48 L milk in total volume:
Explanation48 = 0.8 × V, so V = 60 L. -
Q13 Hard
Mix 25 L (60% milk) with 25 L (80% milk). Milk percentage is:
ExplanationMilk = 15 + 20 = 35 in 50 L = 70%. -
Q14 Easy
36 L mixture, milk : water = 2 : 1. Water is:
ExplanationWater = 1/3 × 36 = 12 L.
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DS1 Easy
How much milk is in the vessel?
Statement IMilk : water = 5 : 3.
Statement IITotal mixture is 32 litres.
ExplanationNeed both: milk = 5/8 × 32 = 20 L. -
DS2 Easy
Is milk more than 70% of the mixture?
Statement IMilk : water = 4 : 1.
Statement II20 L milk and 5 L water are mixed.
ExplanationEach gives 80% milk, which exceeds 70%.
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DS3 Easy
What is the milk : water ratio?
Statement IMilk is 18 L.
Statement IIWater is 12 L.
ExplanationNeed both: ratio = 18 : 12 = 3 : 2. -
DS4 Medium
How much water must be added?
Statement IVessel has 18 L milk in 30 L total.
Statement IIFinal milk concentration must be 60%.
ExplanationStatement I alone: already 60%, so 0 L water needed.