A container has 30 litres of water. If 3 litres of water is replaced by 3 litres of spririt and this operation is repeated twice, then what will be the quantity of water in the new mixture?

Options

A. 24
B. 23
C. 24.3
D. 23.3

Answer

To solve the problem step by step, we will analyze the operations performed on the container with water and spirit.

### Step 1: Initial Setup
- We start with a container that has **30 liters of water** and **0 liters of spirit**.

### Step 2: First Replacement
- We replace **3 liters of water** with **3 liters of spirit**.
- After this operation, the quantity of water left in the container is:
\[ 30 \text{ liters (initial water)} - 3 \text{ liters (replaced)} = 27 \text{ liters of water} \]
- The quantity of spirit in the container is now **3 liters**.

### Step 3: Mixture After First Replacement
- The new mixture consists of:
- Water: **27 liters**
- Spirit: **3 liters**
- The total volume remains **30 liters**.

### Step 4: Second Replacement
- Now, we take out **3 liters of the mixture** (which contains both water and spirit).
- The proportion of water in the mixture is:
\[ \text{Proportion of water} = \frac{27 \text{ liters of water}}{30 \text{ liters of mixture}} = \frac{27}{30} = \frac{9}{10} \]
- The amount of water taken out when we remove **3 liters of the mixture** is:
\[ \text{Water taken out} = 3 \text{ liters} \times \frac{9}{10} = 2.7 \text{ liters} \]

### Step 5: Water Remaining After Second Replacement
- After removing **2.7 liters of water**, the amount of water left in the container is:
\[ 27 \text{ liters} - 2.7 \text{ liters} = 24.3 \text{ liters of water} \]
- The spirit remains unchanged at **3 liters**.

### Final Mixture
- After the second replacement, the final quantities in the container are:
- Water: **24.3 liters**
- Spirit: **3 liters**
- The total volume is still **30 liters**.

### Conclusion
- The quantity of water in the new mixture is **24.3 liters**.

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