A man has whisky worth Rs.22 a litre and another lot worth Rs. 18 a litre.Equal quantities of these are mixed with water to obtain a mixture of 50 litres worth Rs. 16 a litre. Find how much water the mixture contains ?

Options

A. 5 litre
B. 10 litre
C. 15 litre
D. 20 litre

Answer

To solve the problem step by step, we will follow the concepts of alligation or mixture.

### Step 1: Understand the components of the mixture
We have two types of whisky:
- Whisky A: worth Rs. 22 per litre
- Whisky B: worth Rs. 18 per litre

We will mix equal quantities of these two whiskies with water to create a total mixture of 50 litres worth Rs. 16 per litre.

### Step 2: Set up the equations
Let the quantity of each whisky (A and B) be \( x \) litres. Since we are mixing equal quantities, the total volume of whisky will be \( 2x \) litres. The remaining volume will be water.

The total volume of the mixture is given as 50 litres:
\[ 2x + \text{(volume of water)} = 50 \]

### Step 3: Calculate the total value of the mixture
The total value of the whiskies can be calculated as follows:
- Value from Whisky A: \( 22x \)
- Value from Whisky B: \( 18x \)

The total value of the whisky mixture is:
\[ 22x + 18x = 40x \]

### Step 4: Calculate the value of the entire mixture
The value of the entire 50-litre mixture at Rs. 16 per litre is:
\[ \text{Total value} = 50 \times 16 = 800 \]

### Step 5: Set up the equation for the values
Now we can set up the equation based on the total value:
\[ 40x = 800 \]

### Step 6: Solve for \( x \)
To find \( x \), we divide both sides by 40:
\[ x = \frac{800}{40} = 20 \]

### Step 7: Calculate the volume of whisky and water
Since \( x = 20 \), the volume of each whisky (A and B) is 20 litres. Therefore, the total volume of whisky is:
\[ 2x = 2 \times 20 = 40 \text{ litres} \]

Now, we can find the volume of water:
\[ \text{Volume of water} = 50 - 40 = 10 \text{ litres} \]

### Final Answer
The mixture contains **10 litres of water**.

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