Petrol is 7 times heavy than Kerosene and Castrol mobilis 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. `3:4`
B. `7:4`
C. `9:19`
D. `9:10`

Answer

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

### Step 1: Define the weights of the substances
Let the weight of kerosene be represented as \( k \) (in any unit, say kg).

- The weight of petrol is \( 7k \) (since petrol is 7 times heavier than kerosene).
- The weight of Castrol Mobilis is \( 18k \) (since it is 18 times heavier than kerosene).

### Step 2: Set up the mixture
Let the ratio of petrol to Castrol Mobilis be \( P:M \).

When we mix \( P \) parts of petrol and \( M \) parts of Castrol Mobilis, the total weight of the mixture will be:
\[ \text{Total weight} = P \cdot (7k) + M \cdot (18k) = 7Pk + 18Mk \]

### Step 3: Set the desired weight of the mixture
According to the problem, the new mixture must be 11 times as heavy as kerosene. Therefore, the total weight of the mixture can also be expressed as:
\[ \text{Total weight} = (P + M) \cdot (11k) \]

### Step 4: Equate the two expressions for total weight
Now we can set the two expressions for total weight equal to each other:
\[ 7Pk + 18Mk = (P + M) \cdot (11k) \]

### Step 5: Simplify the equation
Dividing through by \( k \) (assuming \( k \neq 0 \)):
\[ 7P + 18M = 11(P + M) \]

Expanding the right side:
\[ 7P + 18M = 11P + 11M \]

### Step 6: Rearranging the equation
Now, we rearrange the equation to isolate terms involving \( P \) and \( M \):
\[ 7P + 18M - 11P - 11M = 0 \]
\[ -4P + 7M = 0 \]

### Step 7: Solve for the ratio
Now, we can express the ratio \( P:M \):
\[ 4P = 7M \implies \frac{P}{M} = \frac{7}{4} \]

Thus, the ratio of petrol to Castrol Mobilis in the mixture is:
\[ \text{Ratio of petrol to Castrol Mobilis} = 7:4 \]

### Final Answer
The ratio of petrol to Castrol Mobilis in the new mixture should be \( 7:4 \).

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