A bartender stole champagne from a bottle that contained 50% of spirit and he replaced what he had stolen with champagne having 20% spirit. The bottle then contained only 25% spirit. How much of the bottle did he steal?

Options

A. 0.8
B. 0.8333
C. 0.8571
D. 0.8888

Answer

To solve the problem step by step, we will use the concept of alligation.

### Step 1: Understand the problem
We have a bottle that originally contains a mixture of 50% spirit. The bartender steals some amount of this mixture and replaces it with champagne that has 20% spirit. After this process, the final mixture in the bottle contains 25% spirit. We need to find out how much of the original mixture the bartender stole.

### Step 2: Set up the alligation
We will set up an alligation to find the ratio of the quantities of the original mixture and the champagne:

- Original mixture (stolen): 50% spirit
- Champagne (replacement): 20% spirit
- Final mixture: 25% spirit

### Step 3: Calculate the differences
Now, we calculate the differences:

- Difference between the original mixture and the final mixture:
\[ 50\% - 25\% = 25\% \]

- Difference between the champagne and the final mixture:
\[ 25\% - 20\% = 5\% \]

### Step 4: Set up the ratio
Now we can set up the ratio of the quantities using these differences:

- The ratio of the original mixture (50% spirit) to the champagne (20% spirit) is:
\[ \text{Ratio} = \frac{25}{5} = 5:1 \]

### Step 5: Determine the total parts
The total parts in the mixture is:
\[ 5 + 1 = 6 \]

### Step 6: Determine the amount stolen
Let the total volume of the bottle be \( V \). The amount stolen (which corresponds to the part of the original mixture) is:
\[ \text{Amount stolen} = \frac{5}{6} \times V \]

### Step 7: Conclusion
Thus, the bartender stole \(\frac{5}{6}\) of the total volume of the bottle.