Vessel-A contains 80 liters mixture of petrol and kerosene oil in the ratio 3 : 1 and vessel-B contains mixture of diesel, petrol and kerosene oil in the ratio 1:3:5. Mixtures of both vessels are mixed in another vessel-C and quantity of petrol in vessel-C is 10 liters more than the quantity of kerosene oil in vessel-C. Then, find the capacity of vessel-B.

Options

A. 140 litres
B. 135 litres
C. 120 litres
D. 125 litres

Answer

To solve the problem step by step, we will break down the information given and apply the necessary calculations.

### Step 1: Determine the quantities in Vessel A
Vessel A contains a mixture of petrol and kerosene oil in the ratio of 3:1, with a total volume of 80 liters.

- **Total parts in the ratio** = 3 + 1 = 4 parts
- **Quantity of petrol in Vessel A** = (3/4) * 80 = 60 liters
- **Quantity of kerosene oil in Vessel A** = (1/4) * 80 = 20 liters

### Step 2: Define the quantities in Vessel B
Vessel B contains a mixture of diesel, petrol, and kerosene oil in the ratio of 1:3:5. Let the quantities of diesel, petrol, and kerosene oil be represented as follows:

- **Diesel** = y liters
- **Petrol** = 3y liters
- **Kerosene oil** = 5y liters

### Step 3: Set up the equation for Vessel C
When the mixtures from Vessel A and Vessel B are combined in Vessel C, the total quantities of petrol and kerosene oil will be:

- **Total petrol in Vessel C** = Quantity of petrol from A + Quantity of petrol from B = 60 + 3y
- **Total kerosene oil in Vessel C** = Quantity of kerosene oil from A + Quantity of kerosene oil from B = 20 + 5y

According to the problem, the quantity of petrol in Vessel C is 10 liters more than the quantity of kerosene oil in Vessel C:

\[ 60 + 3y = (20 + 5y) + 10 \]

### Step 4: Solve the equation
Now, simplify the equation:

1. Rearranging gives:
\[ 60 + 3y = 30 + 5y \]

2. Subtracting 3y from both sides:
\[ 60 = 30 + 2y \]

3. Subtracting 30 from both sides:
\[ 30 = 2y \]

4. Dividing by 2:
\[ y = 15 \]

### Step 5: Calculate the capacity of Vessel B
Now that we have the value of y, we can find the total capacity of Vessel B:

- **Diesel** = y = 15 liters
- **Petrol** = 3y = 3 * 15 = 45 liters
- **Kerosene oil** = 5y = 5 * 15 = 75 liters

Total capacity of Vessel B:
\[ \text{Total capacity} = y + 3y + 5y = 15 + 45 + 75 = 135 \text{ liters} \]

### Final Answer
The capacity of Vessel B is **135 liters**.

---