Mixing Milk-Water & Two Costs
Milk-Water और दो Costs का Mixing
Mixing Milk-Water & Two Costs
- Mixture & Alligation
- Mixing Milk-Water & Two Costs
Handle milk-water ratio changes, profit by selling diluted milk at cost, and combining two mixtures.
🎯 Learning Objective
Handle milk-water ratio changes, profit by selling diluted milk at cost, and combining two mixtures.
💡 Concept
- In a mixture with ratio a : b, the quantity of each part = (its share / total parts) × total volume.
- Adding pure water changes only the water amount — milk stays the same; re-solve for the new ratio.
- Selling milk-water at the cost price of pure milk gives profit% = (water / milk) × 100.
- To blend two mixtures to a target strength, use alligation on their milk-fractions.
- Always convert ratios to actual quantities when volumes are given.
🧮 Key Formulas
Part quantity = (share / total parts) × volume
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Profit% (diluted milk sold at cost) = (water / milk) × 100
✏️ Easy Example
Q. A 40 L mixture has milk and water in ratio 3 : 2. How many litres of milk does it contain?
- Total parts = 3 + 2 = 5
- Milk = 3/5 × 40 = 24 L
- (Water = 2/5 × 40 = 16 L)
Answer: 24 L of milk
🇮🇳 Real-Life Example
A doodhwala on the Mumbai local route sells milk mixed with water at the full milk price — the water-to-milk ratio is exactly his profit margin, and buyers use this maths to check him.
📝 Exam-Level Example
Q. A 40 L mixture has milk : water = 3 : 2. How much water must be added to make the ratio 3 : 4?
- Milk = 3/5 × 40 = 24 L, water = 16 L
- Milk stays 24 L. Let x litres of water be added.
- New ratio: 24 / (16 + x) = 3 / 4
- Cross-multiply: 96 = 3(16 + x) → 96 = 48 + 3x
- 3x = 48 → x = 16
Answer: Add 16 L of water
📝 Exam-Level Example
Q. Two vessels have milk : water in ratios 4 : 3 and 2 : 3. In what ratio should they be mixed to get milk : water = 1 : 1?
- Milk fraction in A = 4/7, in B = 2/5, target = 1/2
- By alligation, A : B = (1/2 − 2/5) : (4/7 − 1/2)
- = (1/10) : (1/14)
- Multiply through by 70: = 7 : 5
- Check: milk = 7×(4/7) + 5×(2/5) = 4 + 2 = 6; water = 3 + 3 = 6 → 1 : 1 ✓
Answer: Mix vessel A and B in the ratio 7 : 5
🪄 Memory Trick
For diluted milk sold at cost, profit% = water/milk × 100. So 25% profit means water : milk = 1 : 4 — no long calculation needed.
⚠️ Common Mistakes
- ❌ Changing the milk amount when only water is added
- ❌ Using ratios directly in alligation instead of the milk-fractions
- ❌ Forgetting to convert the final ratio into litres when a volume is given
🏆 Exam Tips
- ✅ When water is added, freeze the milk value and solve for the new denominator
- ✅ For two-mixture blends, always work with the milk fraction of each
📌 Summary
- Part quantity = share/total × volume
- Adding water: milk fixed, re-solve ratio
- Diluted milk at cost → profit% = water/milk × 100
- Blend two mixtures via alligation on milk-fractions