The concnetration of petrol is three different mixtures (petrol and kerosene) is `1/2, 3/5` and `4/5` respectively. If 2 litres, 3 litres and 1 litre are taken from these different vessels and mixed. What is the ratio of petrol and Kerosone in the new mixture?

Options

A. `4:5`
B. `3:2`
C. `3:5`
D. `2:3`

Answer

To solve the problem, we need to find the ratio of petrol to kerosene in the new mixture formed by mixing 2 litres from the first vessel, 3 litres from the second vessel, and 1 litre from the third vessel.

### Step-by-Step Solution:

1. **Identify the Concentrations:**
- Vessel A (2 litres): Concentration of petrol = \( \frac{1}{2} \)
- Vessel B (3 litres): Concentration of petrol = \( \frac{3}{5} \)
- Vessel C (1 litre): Concentration of petrol = \( \frac{4}{5} \)

2. **Calculate the Amount of Petrol from Each Vessel:**
- From Vessel A:
\[ \text{Petrol from A} = 2 \text{ litres} \times \frac{1}{2} = 1 \text{ litre} \]
- From Vessel B:
\[ \text{Petrol from B} = 3 \text{ litres} \times \frac{3}{5} = \frac{9}{5} \text{ litres} = 1.8 \text{ litres} \]
- From Vessel C:
\[ \text{Petrol from C} = 1 \text{ litre} \times \frac{4}{5} = 0.8 \text{ litres} \]

3. **Total Amount of Petrol:**
\[ \text{Total Petrol} = 1 + 1.8 + 0.8 = 3.6 \text{ litres} \]

4. **Calculate the Total Volume of the Mixture:**
\[ \text{Total Volume} = 2 + 3 + 1 = 6 \text{ litres} \]

5. **Calculate the Amount of Kerosene:**
- Since the total volume of the mixture is 6 litres and we have 3.6 litres of petrol, the amount of kerosene can be calculated as:
\[ \text{Total Kerosene} = \text{Total Volume} - \text{Total Petrol} = 6 - 3.6 = 2.4 \text{ litres} \]

6. **Find the Ratio of Petrol to Kerosene:**
\[ \text{Ratio of Petrol to Kerosene} = \frac{\text{Total Petrol}}{\text{Total Kerosene}} = \frac{3.6}{2.4} \]
- Simplifying this ratio:
\[ \frac{3.6}{2.4} = \frac{36}{24} = \frac{3}{2} \]

### Final Answer:
The ratio of petrol to kerosene in the new mixture is \( 3:2 \).