In a mixture of petrol ankd Kerosence petrol is only 99 litres. If this same quantity of petrol would be presented in another mixture of petrol and Kerosene where total volume would be 198 litres less than actual mixture then the concentration of pettol in the actual mixture woudl have been 13.33% point less than that of the new mixture. What is the concentration of petrol in actual mixture?

Options

A. a. 0.2
B. b. 0.1666
C. c. 0.2666
D. d. 0.0833

Answer

To find the concentration of petrol in the actual mixture, we can follow these steps:

### Step 1: Define the variables
Let:
- \( P = 99 \) liters (the amount of petrol in the actual mixture)
- \( K \) = amount of kerosene in the actual mixture
- \( T = P + K \) = total volume of the actual mixture

### Step 2: Set up the equations
From the problem, we know:
- The total volume of the actual mixture is \( T = 99 + K \).
- The new mixture has a total volume that is 198 liters less than the actual mixture, so:
\[ T_{new} = T - 198 = (99 + K) - 198 = K - 99 \]

### Step 3: Find the concentration of petrol in both mixtures
1. **Concentration of petrol in the actual mixture**:
\[ C_{actual} = \frac{P}{T} \times 100 = \frac{99}{99 + K} \times 100 \]

2. **Concentration of petrol in the new mixture**:
In the new mixture, the amount of petrol remains the same (99 liters), and the total volume is \( K - 99 \):
\[ C_{new} = \frac{P}{T_{new}} \times 100 = \frac{99}{K - 99} \times 100 \]

### Step 4: Set up the equation based on the given condition
According to the problem, the concentration of petrol in the actual mixture is 13.33% less than that in the new mixture:
\[ C_{actual} = C_{new} - 13.33\% \]
Substituting the expressions for \( C_{actual} \) and \( C_{new} \):
\[ \frac{99}{99 + K} \times 100 = \left(\frac{99}{K - 99} \times 100\right) - 13.33 \]

### Step 5: Solve the equation
1. Multiply through by \( (99 + K)(K - 99) \) to eliminate the denominators:
\[ 99(K - 99) \times 100 = 99(99 + K) \times 100 - 13.33(99 + K)(K - 99) \]
2. Simplify and solve for \( K \):
- This will lead to a quadratic equation in terms of \( K \).

### Step 6: Calculate the concentration of petrol in the actual mixture
Once you find \( K \), substitute it back into the formula for \( C_{actual} \):
\[ C_{actual} = \frac{99}{99 + K} \times 100 \]

### Step 7: Final Calculation
After solving the equation, you will find a specific value for \( K \), allowing you to calculate \( C_{actual} \).