What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three identical vessels in the ratio 4:1, 5 : 2 and 6:1, respectively?

Options

A. `166 : 22`
B. `83 : 22`
C. `83 : 44`
D. None of these

Answer

To solve the problem of finding the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene from three identical vessels, we will follow these steps:

### Step 1: Understand the Ratios in Each Vessel
We have three vessels with the following ratios of petrol to kerosene:
- Vessel A: 4:1
- Vessel B: 5:2
- Vessel C: 6:1

### Step 2: Determine the Total Parts in Each Vessel
For each vessel, we can determine the total parts of the mixture:
- Vessel A: 4 (petrol) + 1 (kerosene) = 5 parts
- Vessel B: 5 (petrol) + 2 (kerosene) = 7 parts
- Vessel C: 6 (petrol) + 1 (kerosene) = 7 parts

### Step 3: Assign a Common Capacity to Each Vessel
Since the vessels are identical, we can assign a common capacity. Let’s assume each vessel has a capacity of 35 units (this is a convenient number that is a multiple of the total parts).

### Step 4: Calculate the Amount of Petrol and Kerosene in Each Vessel
Now, we will calculate the amount of petrol and kerosene in each vessel based on the assumed capacity of 35 units.

- For Vessel A (4:1 ratio):
- Total parts = 5
- Petrol = (4/5) * 35 = 28 units
- Kerosene = (1/5) * 35 = 7 units

- For Vessel B (5:2 ratio):
- Total parts = 7
- Petrol = (5/7) * 35 = 25 units
- Kerosene = (2/7) * 35 = 10 units

- For Vessel C (6:1 ratio):
- Total parts = 7
- Petrol = (6/7) * 35 = 30 units
- Kerosene = (1/7) * 35 = 5 units

### Step 5: Sum Up the Amounts of Petrol and Kerosene
Now, we will sum up the amounts of petrol and kerosene from all three vessels:
- Total Petrol = 28 (from A) + 25 (from B) + 30 (from C) = 83 units
- Total Kerosene = 7 (from A) + 10 (from B) + 5 (from C) = 22 units

### Step 6: Calculate the Final Ratio
Finally, we can find the ratio of petrol to kerosene:
- Ratio of Petrol to Kerosene = Total Petrol : Total Kerosene = 83 : 22

### Final Answer
The ratio of petrol to kerosene in the final solution is **83:22**.

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