Petrol is 7 times heavy than Kerosene and Castrol mobil is 18 times as heavy as Kerosene. What should be the ratio of petrol and mobil in the new mixture to get the mixture which must be 11 times as heavy as kerosene?

Options

A. 0.7368421052631
B. 0.29444444444444
C. 0.38819444444444
D. 0.38194444444444

Answer

To solve the problem, we need to find the ratio of petrol and Castrol mobil to create a mixture that is 11 times as heavy as kerosene. Let's break down the solution step by step.

### Step 1: Define the weights
Let the weight of kerosene be \( K \).
- The weight of petrol is \( 7K \) (since petrol is 7 times heavier than kerosene).
- The weight of Castrol mobil is \( 18K \) (since Castrol mobil is 18 times heavier than kerosene).

### Step 2: Set up the equation for the mixture
We want the mixture of petrol and Castrol mobil to be 11 times heavier than kerosene. Therefore, the total weight of the mixture should be:
\[ \text{Weight of mixture} = 11K \]

### Step 3: Let the quantities of petrol and mobil be \( x \) and \( y \) respectively
The total weight of the mixture can be expressed as:
\[ 7x + 18y = 11K \]

### Step 4: Express \( K \) in terms of \( x \) and \( y \)
From the equation above, we can express \( K \) as:
\[ K = \frac{7x + 18y}{11} \]

### Step 5: Find the ratio of petrol to mobil
To find the ratio of petrol to mobil, we can use the concept of alligation. We will consider the weights of each component and the desired weight of the mixture.

1. **Weight of petrol**: \( 7 \)
2. **Weight of Castrol mobil**: \( 18 \)
3. **Desired weight of mixture**: \( 11 \)

### Step 6: Apply alligation
Using alligation, we find the differences:
- Difference between the weight of Castrol mobil and the desired weight:
\[ 18 - 11 = 7 \]
- Difference between the weight of petrol and the desired weight:
\[ 11 - 7 = 4 \]

### Step 7: Set up the ratio
The ratio of petrol to Castrol mobil can be set up as:
\[ \text{Ratio of petrol to mobil} = \frac{4}{7} \]

### Step 8: Final ratio
Thus, the ratio of petrol to Castrol mobil in the mixture is:
\[ \text{Petrol : Castrol mobil} = 4 : 7 \]

### Conclusion
The required ratio of petrol and Castrol mobil in the new mixture is \( 4 : 7 \).

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