The ratio of petrol and kerosene is the container is 3:2 when 10 litres of the mixture is taken out and is replaced by the kerosene, the ratio becomes 2:3. The total quantity of the mixture in the container is :

Options

A. 25
B. 30
C. 45
D. cannot be determined

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Initial Ratio
The initial ratio of petrol to kerosene in the container is given as 3:2. This means that for every 3 parts of petrol, there are 2 parts of kerosene.

### Step 2: Let the Total Quantity be 'x'
Let the total quantity of the mixture in the container be \( x \) liters. According to the ratio:
- Quantity of petrol = \( \frac{3}{5}x \) (since 3 parts out of 5)
- Quantity of kerosene = \( \frac{2}{5}x \) (since 2 parts out of 5)

### Step 3: Remove 10 Liters of the Mixture
When 10 liters of the mixture is taken out, the ratio of petrol to kerosene remains the same (3:2). Therefore, the quantities of petrol and kerosene removed can be calculated as:
- Petrol removed = \( \frac{3}{5} \times 10 = 6 \) liters
- Kerosene removed = \( \frac{2}{5} \times 10 = 4 \) liters

### Step 4: Calculate Remaining Quantities
After removing 10 liters:
- Remaining petrol = \( \frac{3}{5}x - 6 \)
- Remaining kerosene = \( \frac{2}{5}x - 4 \)

### Step 5: Add 10 Liters of Kerosene
Now, we replace the 10 liters removed with kerosene. Thus, the new quantity of kerosene becomes:
- New kerosene = \( \left(\frac{2}{5}x - 4\right) + 10 = \frac{2}{5}x + 6 \)

### Step 6: Set Up the New Ratio
After adding kerosene, the new ratio of petrol to kerosene is given as 2:3. Therefore, we can set up the equation:
\[ \frac{\text{Remaining Petrol}}{\text{New Kerosene}} = \frac{2}{3} \]
Substituting the values:
\[ \frac{\frac{3}{5}x - 6}{\frac{2}{5}x + 6} = \frac{2}{3} \]

### Step 7: Cross-Multiply to Solve for x
Cross-multiplying gives:
\[ 3\left(\frac{3}{5}x - 6\right) = 2\left(\frac{2}{5}x + 6\right) \]
Expanding both sides:
\[ \frac{9}{5}x - 18 = \frac{4}{5}x + 12 \]

### Step 8: Rearranging the Equation
Rearranging the equation to isolate \( x \):
\[ \frac{9}{5}x - \frac{4}{5}x = 12 + 18 \]
\[ \frac{5}{5}x = 30 \]
\[ x = 30 \text{ liters} \]

### Conclusion
The total quantity of the mixture in the container is **30 liters**.

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