From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was :

Options

A. 75 litres
B. 100 litres
C. 150 litres
D. 120 litres

Answer

To solve the problem step by step, we will analyze the situation where a thief steals wine from a container and replaces it with water, and we need to find the initial amount of wine in the container.

### Step 1: Understand the problem
The thief steals 15 liters of wine and replaces it with the same quantity of water. This process is repeated three times, and after these three attempts, the ratio of wine to water in the container is given as 343:169.

### Step 2: Set up the ratios
After three attempts, the ratio of wine to the total mixture (wine + water) is 343:512. This is because the total mixture consists of the wine and the water added back in. The total parts of the mixture can be calculated as:
- Wine parts = 343
- Water parts = 169
- Total parts = 343 + 169 = 512

### Step 3: Find the ratio after one attempt
To find the ratio after one attempt, we take the cube root of the ratios after three attempts:
- Wine after three attempts = 343
- Total mixture after three attempts = 512

Thus, the ratio after one attempt is:
- Wine : Total mixture = \( \sqrt[3]{343} : \sqrt[3]{512} \)
- This simplifies to \( 7 : 8 \)

### Step 4: Interpret the ratio
From the ratio \( 7 : 8 \), we can conclude that out of 8 parts of the total mixture, 7 parts are wine and 1 part is water. Since the thief stole 15 liters of wine, this 1 part represents the quantity of wine that was stolen.

### Step 5: Calculate the total initial amount of wine
We know that 1 part corresponds to the 15 liters that were stolen. Therefore, if 1 part = 15 liters, then:
- 8 parts (the total mixture) = \( 15 \times 8 = 120 \) liters

Thus, the initial amount of wine in the container was 120 liters.

### Final Answer
The initial amount of wine in the container was **120 liters**.

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