The liquids, X and Y are mixed in the ratio of 3:2 and the mixture is sold at Rs 11 per litre at a profit of 10%. If the liquid X costs Rs. 2 more per litre than Y, the cost of X per litre is (in Rs.)

Options

A. 10.8
B. 11.75
C. 9.5
D. 11

Answer

To solve the problem step by step, we will use the information given in the question.

### Step 1: Understand the ratio of the liquids
We have two liquids, X and Y, mixed in the ratio of 3:2. This means for every 3 parts of liquid X, there are 2 parts of liquid Y.

### Step 2: Determine the selling price and profit
The mixture is sold at Rs 11 per litre with a profit of 10%. To find the cost price (CP) of the mixture, we can use the formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Given that the profit is 10% of the cost price, we can express the selling price as:
\[ SP = CP + 0.1 \times CP = 1.1 \times CP \]
Setting SP to Rs 11, we have:
\[ 11 = 1.1 \times CP \]
To find CP, we rearrange the equation:
\[ CP = \frac{11}{1.1} = 10 \text{ Rs} \]

### Step 3: Set up the cost equations for liquids X and Y
Let the cost of liquid Y be Rs \(y\) per litre. Since liquid X costs Rs 2 more than liquid Y, we can express the cost of liquid X as:
\[ \text{Cost of X} = y + 2 \]

### Step 4: Calculate the total cost of the mixture
The total cost of the mixture can be calculated based on the ratio of the liquids:
- For 3 parts of X: \(3 \times (y + 2)\)
- For 2 parts of Y: \(2 \times y\)

The total cost of the mixture is:
\[ \text{Total Cost} = 3(y + 2) + 2y = 3y + 6 + 2y = 5y + 6 \]

### Step 5: Relate the total cost to the cost price
Since we found the cost price of the mixture to be Rs 10, we can set up the equation:
\[ \frac{5y + 6}{5} = 10 \]
Multiplying through by 5 to eliminate the fraction gives:
\[ 5y + 6 = 50 \]
Subtracting 6 from both sides:
\[ 5y = 44 \]
Dividing by 5:
\[ y = \frac{44}{5} = 8.8 \text{ Rs} \]

### Step 6: Calculate the cost of liquid X
Now that we have the cost of liquid Y, we can find the cost of liquid X:
\[ \text{Cost of X} = y + 2 = 8.8 + 2 = 10.8 \text{ Rs} \]

### Conclusion
The cost of liquid X per litre is Rs 10.8.