Two vessels contain spirit of `0.5 and 0.75` concentrations. If 2 lt from the first vessel and 3 lt from the second vessel are mixed, then what will be the ratio of the spirit and the water in the resultant solution?

Answer

To solve the problem step by step, we will find the ratio of spirit to water in the resultant mixture after mixing the two solutions.

### Step 1: Identify the concentrations and volumes
- The first vessel has a spirit concentration of 0.5 (50%).
- The second vessel has a spirit concentration of 0.75 (75%).
- We are mixing 2 liters from the first vessel and 3 liters from the second vessel.

### Step 2: Calculate the amount of spirit in each vessel
- For the first vessel (0.5 concentration):
\[ \text{Amount of spirit} = \text{Volume} \times \text{Concentration} = 2 \, \text{liters} \times 0.5 = 1 \, \text{liter} \]

- For the second vessel (0.75 concentration):
\[ \text{Amount of spirit} = \text{Volume} \times \text{Concentration} = 3 \, \text{liters} \times 0.75 = 2.25 \, \text{liters} \]

### Step 3: Calculate the total amount of spirit in the mixture
- Total spirit in the mixture:
\[ \text{Total spirit} = 1 \, \text{liter} + 2.25 \, \text{liters} = 3.25 \, \text{liters} \]

### Step 4: Calculate the total volume of the mixture
- Total volume of the mixture:
\[ \text{Total volume} = 2 \, \text{liters} + 3 \, \text{liters} = 5 \, \text{liters} \]

### Step 5: Calculate the amount of water in the mixture
- Amount of water in the mixture:
\[ \text{Water} = \text{Total volume} - \text{Total spirit} = 5 \, \text{liters} - 3.25 \, \text{liters} = 1.75 \, \text{liters} \]

### Step 6: Find the ratio of spirit to water
- The ratio of spirit to water:
\[ \text{Ratio} = \frac{\text{Spirit}}{\text{Water}} = \frac{3.25}{1.75} \]

- Simplifying the ratio:
\[ \text{Ratio} = \frac{3.25 \times 4}{1.75 \times 4} = \frac{13}{7} \]

### Final Answer
The ratio of spirit to water in the resultant mixture is **13:7**.

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