The concentration of petrol in 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 three different vessels and mixed. What is the ratio of petrol and kerosene in the new mixture?

Options

A. 0.17013888888889
B. 0.12638888888889
C. 0.12847222222222
D. 0.085416666666667

Answer

To solve the problem, we need to find the ratio of petrol and kerosene in the new mixture after mixing the specified amounts from the three different vessels. Let's break it down step by step.

### Step 1: Determine the amount of petrol and kerosene in each mixture.

1. **First Mixture (1/2 petrol)**:
- Concentration: \( \frac{1}{2} \) means 1 part petrol and 1 part kerosene.
- Total parts = 1 (petrol) + 1 (kerosene) = 2 parts.
- From 2 liters taken, petrol = \( \frac{1}{2} \times 2 = 1 \) liter, kerosene = \( \frac{1}{2} \times 2 = 1 \) liter.

2. **Second Mixture (3/5 petrol)**:
- Concentration: \( \frac{3}{5} \) means 3 parts petrol and 2 parts kerosene.
- Total parts = 3 (petrol) + 2 (kerosene) = 5 parts.
- From 3 liters taken, petrol = \( \frac{3}{5} \times 3 = \frac{9}{5} = 1.8 \) liters, kerosene = \( \frac{2}{5} \times 3 = \frac{6}{5} = 1.2 \) liters.

3. **Third Mixture (4/5 petrol)**:
- Concentration: \( \frac{4}{5} \) means 4 parts petrol and 1 part kerosene.
- Total parts = 4 (petrol) + 1 (kerosene) = 5 parts.
- From 1 liter taken, petrol = \( \frac{4}{5} \times 1 = \frac{4}{5} = 0.8 \) liters, kerosene = \( \frac{1}{5} \times 1 = \frac{1}{5} = 0.2 \) liters.

### Step 2: Calculate the total amount of petrol and kerosene in the new mixture.

- **Total Petrol**:
- From first mixture: 1 liter
- From second mixture: 1.8 liters
- From third mixture: 0.8 liters
- Total Petrol = \( 1 + 1.8 + 0.8 = 3.6 \) liters.

- **Total Kerosene**:
- From first mixture: 1 liter
- From second mixture: 1.2 liters
- From third mixture: 0.2 liters
- Total Kerosene = \( 1 + 1.2 + 0.2 = 2.4 \) liters.

### Step 3: Find the ratio of petrol to kerosene.

- Ratio of Petrol to Kerosene = \( \frac{Total \, Petrol}{Total \, Kerosene} = \frac{3.6}{2.4} \).

- 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**.

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