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This problem is about mixing milk and water between two containers, P and Q, and calculating the final ratio of milk in container P to water in container Q.

### Step-by-step breakdown:
1. **Initial contents:**
   - Container P: 50 liters of milk.
   - Container Q: 32 liters of water.

2. **Step 1 (Transfer of 10 liters from P to Q):**
   - 10 liters of milk is taken from container P and poured into container Q.
   - New content in P: \(50 - 10 = 40\) liters of milk.
   - New content in Q: \(32\) liters of water + \(10\) liters of milk = 42 liters (mix of milk and water).

3. **Step 2 (Transfer 8 liters of mixture from Q to P):**
   - The total volume in Q is now 42 liters (which is a mixture of milk and water).
   - The proportion of milk in Q is \( \frac{10}{42} \) and the proportion of water is \( \frac{32}{42} \).
   - From Q, 8 liters of mixture is taken out and poured into P. The amount of milk and water in these 8 liters is calculated as follows:
     - Milk in 8 liters: \( \frac{10}{42} \times 8 = 1.9 \) liters (approximately).
     - Water in 8 liters: \( \frac{32}{42} \times 8 = 6.1 \) liters (approximately).

   - After pouring this back into P:
     - Milk in P: \( 40 + 1.9 = 41.9 \) liters.
     - Water in P: 6.1 liters (added from Q's mixture).

   - In Q:
     - Remaining milk: \( 10 - 1.9 = 8.1 \) liters.
     - Remaining water: \( 32 - 6.1 = 25.9 \) liters.

4. **Final Ratios:**
   - Milk in P: 41.9 liters.
   - Water in Q: 25.9 liters.
   - The ratio of milk in P to water in Q is approximately \( 41.9 : 25.9 \).
   - Simplifying this ratio gives approximately \( 99 : 89 \).

### Correct Answer: **Option 4: 99 : 89**

Would you like more details on this process or have further questions?

### Follow-up Questions:
1. What would the ratio be if 5 liters of milk were transferred from P to Q instead?
2. How would the answer change if 12 liters of the mixture were transferred from Q to P?
3. What if Q initially had 40 liters of water instead of 32 liters?
4. How would the solution change if both containers started with 50 liters each?
5. What if 15 liters were transferred in both steps instead of 10 and 8 liters?

### Tip:
When solving problems involving mixtures, carefully track how much of each component (milk or water) is transferred to avoid confusion.

दो बर्तन P और Q हैं। बर्तन P में 50 लीटर दूध है और बर्तन Q में 32 लीटर पानी है। बर्तन P से, 10 लीटर दूध निकाला जाता है और बर्तन Q में डाला जाता है। फिर, बर्तन Q से 8 लीटर मिश्रण (दूध और पानी) निकाला जाता है और बर्तन P में डाला जाता है। बर्तन P में दूध की मात्रा और बर्तन Q में पानी की मात्रा का अनुपात क्या है?

Solve a complex mixture problem involving the transfer of milk and water between two containers, P and Q. Learn how to calculate the final ratio of milk in P to water in Q using step-by-step methods. Suitable for Grades 8-10.

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