A 75-litre mixture contains milk and water in the ratio 3 : 2. If 15 litres of this mixture are removed and replaced with 10 litr…

Question

A 75-litre mixture contains milk and water in the ratio 3 : 2. If 15 litres of this mixture are removed and replaced with 10 litres of pure milk, what is the new ratio of milk to water in the mixture?

1. A. 11 : 7
2. B. 23 : 12 (Correct answer)
3. C. 17 : 11
4. D. 19 : 12

Correct Answer

Option B — 23 : 12

Detailed Solution & Explanation

The correct answer is 23 : 12.

Key Points

• Start from the original 75 litres in the ratio 3 : 2 → milk 45 L, water 30 L.
• Removing 15 L of the mixture removes both in the same 3 : 2 ratio: 9 L milk and 6 L water.
  • Remaining: milk 36 L, water 24 L
• Adding 10 L of pure milk raises milk only:
  • Milk = 36 + 10 = 46 L, water = 24 L
• New ratio = 46 : 24 = 23 : 12.

Additional Information

• The essential point is that removing *mixture* takes both liquids proportionally, whereas the addition affects only one — treating the removal as milk-only is the intended trap.
• Note the total is no longer 75 L: 15 L left and only 10 L returned, so the final volume is 70 L.
• Where the same quantity is removed and replaced repeatedly, use Final = Initial × (1 − x/T)ⁿ instead; that formula applies only when the volume stays constant, which is not the case here.

प्रश्न (हिन्दी में)

75 लीटर के मिश्रण में दूध और पानी का अनुपात 3 : 2 है। यदि इस मिश्रण में से 15 लीटर निकाल दिया जाए और उसकी जगह 10 लीटर शुद्ध दूध डाल दिया जाए, तो मिश्रण में दूध और पानी का नया अनुपात क्या होगा?

1. A. 11 : 7
2. B. 23 : 12
3. C. 17 : 11
4. D. 19 : 12