A vessel of capacity 2 litre is 25% alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessle of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of mixture?

Options

A. `31%`
B. `71%`
C. `49%`
D. `29%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the amount of alcohol in the first vessel (2 liters at 25% alcohol)
- The first vessel has a capacity of 2 liters and contains 25% alcohol.
- To find the amount of alcohol, we calculate:
\[ \text{Amount of alcohol} = \text{Total volume} \times \text{Percentage of alcohol} = 2 \, \text{liters} \times \frac{25}{100} = 0.5 \, \text{liters} \]

### Step 2: Calculate the amount of alcohol in the second vessel (6 liters at 40% alcohol)
- The second vessel has a capacity of 6 liters and contains 40% alcohol.
- To find the amount of alcohol, we calculate:
\[ \text{Amount of alcohol} = \text{Total volume} \times \text{Percentage of alcohol} = 6 \, \text{liters} \times \frac{40}{100} = 2.4 \, \text{liters} \]

### Step 3: Calculate the total amount of alcohol from both vessels
- Now, we add the amounts of alcohol from both vessels:
\[ \text{Total alcohol} = 0.5 \, \text{liters} + 2.4 \, \text{liters} = 2.9 \, \text{liters} \]

### Step 4: Determine the total volume of the mixture
- The total volume of liquid poured into the new vessel is the sum of the capacities of both vessels:
\[ \text{Total volume} = 2 \, \text{liters} + 6 \, \text{liters} = 8 \, \text{liters} \]
- Since the new vessel has a capacity of 10 liters, the remaining space will be filled with water:
\[ \text{Volume of water} = 10 \, \text{liters} - 8 \, \text{liters} = 2 \, \text{liters} \]

### Step 5: Calculate the new concentration of the mixture
- The new concentration of alcohol in the total mixture (which now includes water) is calculated as follows:
\[ \text{New concentration} = \frac{\text{Total alcohol}}{\text{Total volume}} \times 100 = \frac{2.9 \, \text{liters}}{10 \, \text{liters}} \times 100 = 29\% \]

### Final Answer
The new concentration of the mixture is **29%**.

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