A butler stole wine from a butt of sherry which contains 15% of spirit and he replaced what he had stolen by wine containing 6% of spirit.The butt was then 9% strong only.How much of the butt did he steal?

Options

A. `2/3`
B. `1/3`
C. `2/5`
D. `3/5`

Answer

To solve the problem, we will use the method of allegation. Let's break it down step by step.

### Step 1: Understand the Problem
We have a butt of sherry containing 15% spirit. The butler steals some wine and replaces it with wine containing 6% spirit. After this replacement, the mixture has a spirit concentration of 9%. We need to find out how much wine the butler stole from the butt.

### Step 2: Set Up the Allegation
We will apply the allegation method to find the ratio of the quantities of the two different types of wine.

1. The percentage of spirit in the original wine (before theft) = 15%
2. The percentage of spirit in the wine that was added (after theft) = 6%
3. The percentage of spirit in the final mixture = 9%

### Step 3: Calculate the Differences
Using the allegation method, we calculate the differences:

- Difference between the original wine and the final mixture:
\[ 15\% - 9\% = 6\% \]

- Difference between the added wine and the final mixture:
\[ 9\% - 6\% = 3\% \]

### Step 4: Set Up the Ratio
Now we can set up the ratio of the quantities of the two types of wine using the differences calculated:

\[ \text{Ratio} = \frac{6}{3} = 2:1 \]

This means for every 2 parts of the wine added (6% spirit), there is 1 part of the original wine (15% spirit).

### Step 5: Total Parts
The total parts in the mixture are:
\[ 2 + 1 = 3 \text{ parts} \]

### Step 6: Determine the Quantity Stolen
Let the total quantity of the butt be \( x \). The quantity of wine that was replaced (added) is 2 parts out of the total 3 parts. Therefore, the quantity stolen by the butler is:

\[ \text{Quantity stolen} = \frac{1}{3} \times x \]

### Step 7: Conclusion
Thus, the butler stole \( \frac{1}{3} \) of the butt of sherry.

### Final Answer
The butler stole \( \frac{1}{3} \) of the butt.

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