A vessel is full of 80Lmilk. If 10L milk is taken out and replaced by same amount of water and further 16L mixture is taken out and replaced by same amount of water and again further 8L mixture is taken out and replaced by same amount of water again further 20L mixture is taken out replaced by same amount of water then at the end of 4th process the amount of water in the mixture?

Options

A. 37.8L
B. 52.4L
C. 42.2L
D. 27.6L

Answer

To solve the problem step by step, we will analyze the situation after each operation of taking out the mixture and replacing it with water.

### Step 1: Initial Setup
- The vessel initially contains **80 liters of milk** and **0 liters of water**.

### Step 2: First Operation
- **10 liters of milk** is taken out.
- Remaining milk = 80 - 10 = **70 liters**.
- Water added = **10 liters**.
- Now, we have **70 liters of milk** and **10 liters of water**.

### Step 3: Second Operation
- **16 liters of the mixture** is taken out.
- The total mixture is now 80 liters (70 liters of milk + 10 liters of water).
- The proportion of milk in the mixture = 70/80 = 0.875.
- Milk taken out = 16 * 0.875 = **14 liters**.
- Remaining milk = 70 - 14 = **56 liters**.
- Water taken out = 16 - 14 = **2 liters**.
- Remaining water = 10 - 2 = **8 liters**.
- After this operation, we have **56 liters of milk** and **8 liters of water**.

### Step 4: Third Operation
- **8 liters of the mixture** is taken out.
- The total mixture is now 64 liters (56 liters of milk + 8 liters of water).
- The proportion of milk in the mixture = 56/64 = 0.875.
- Milk taken out = 8 * 0.875 = **7 liters**.
- Remaining milk = 56 - 7 = **49 liters**.
- Water taken out = 8 - 7 = **1 liter**.
- Remaining water = 8 - 1 = **7 liters**.
- After this operation, we have **49 liters of milk** and **7 liters of water**.

### Step 5: Fourth Operation
- **20 liters of the mixture** is taken out.
- The total mixture is now 56 liters (49 liters of milk + 7 liters of water).
- The proportion of milk in the mixture = 49/56.
- Milk taken out = 20 * (49/56) = **17.5 liters**.
- Remaining milk = 49 - 17.5 = **31.5 liters**.
- Water taken out = 20 - 17.5 = **2.5 liters**.
- Remaining water = 7 - 2.5 = **4.5 liters**.
- After this operation, we have **31.5 liters of milk** and **4.5 liters of water**.

### Final Calculation
- At the end of the fourth process, the total amount of water in the mixture is **4.5 liters**.

### Summary
The amount of water in the mixture after the fourth operation is **4.5 liters**.

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