There are 90 litre casrol and 150 litres CRB mobil oils. The price of castrol is Rs. 80 per litre and price of CRB is Rs. 75 per litre. Equal amount of castrol and CRB is taken out and then CRB is poured out in the vessel of castrol and castrol is poured out in the vessel of CRB. Now the rate of both the mixtures is same. What is the amount of mobil oil taken out from each of the vessel?

Options

A. a. 45 litres
B. b. 56.25 litres
C. c. 24.5 litres
D. d. 36 litres

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total cost of Castrol and CRB oils.
- **Castrol Oil:**
- Volume = 90 liters
- Price per liter = Rs. 80
- Total cost = Volume × Price per liter = 90 × 80 = Rs. 7200

- **CRB Oil:**
- Volume = 150 liters
- Price per liter = Rs. 75
- Total cost = Volume × Price per liter = 150 × 75 = Rs. 11250

### Step 2: Define the amount of oil taken out.
Let the amount of oil taken out from each vessel be **x liters**.

### Step 3: Calculate the new total cost after taking out and mixing the oils.
- **For Castrol:**
- After taking out x liters, the remaining volume = 90 - x liters.
- The cost of the remaining Castrol oil = (90 - x) × 80 = 7200 - 80x.
- When x liters of CRB oil (cost Rs. 75 per liter) is added, the total cost becomes:
- Total cost of Castrol mixture = (7200 - 80x) + (75x) = 7200 - 80x + 75x = 7200 - 5x.

- **For CRB:**
- After taking out x liters, the remaining volume = 150 - x liters.
- The cost of the remaining CRB oil = (150 - x) × 75 = 11250 - 75x.
- When x liters of Castrol oil (cost Rs. 80 per liter) is added, the total cost becomes:
- Total cost of CRB mixture = (11250 - 75x) + (80x) = 11250 - 75x + 80x = 11250 + 5x.

### Step 4: Calculate the average cost per liter for both mixtures.
- **Average cost of Castrol mixture:**
- Average cost = Total cost / Total volume = (7200 - 5x) / 90.

- **Average cost of CRB mixture:**
- Average cost = Total cost / Total volume = (11250 + 5x) / 150.

### Step 5: Set the average costs equal to each other.
Since the average costs are equal:
\[ \frac{7200 - 5x}{90} = \frac{11250 + 5x}{150} \]

### Step 6: Cross-multiply to solve for x.
Cross-multiplying gives:
\[ 150(7200 - 5x) = 90(11250 + 5x) \]
Expanding both sides:
\[ 1080000 - 750x = 1012500 + 450x \]

### Step 7: Combine like terms.
Bringing all terms involving x to one side and constant terms to the other side:
\[ 1080000 - 1012500 = 750x + 450x \]
\[ 67500 = 1200x \]

### Step 8: Solve for x.
\[ x = \frac{67500}{1200} = 56.25 \text{ liters} \]

### Final Answer:
The amount of mobil oil taken out from each vessel is **56.25 liters**.

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