A mixture of a certain quantity of milk with 16 litres of water is worth 90 paise per litre. If pure milk be worth Rs. 1.80 per litre. How much milk is there in the mixture ?

Options

A. 16
B. 70
C. 80
D. 90

Answer

To solve the problem step by step, we will use the concept of alligation.

### Step 1: Understand the given values
- The cost of pure milk = Rs. 1.80 per litre
- The cost of water = Rs. 0 (since water is free)
- The cost of the mixture = Rs. 0.90 per litre
- The quantity of water = 16 litres

### Step 2: Set up the alligation
We will use the alligation method to find the ratio of milk to water in the mixture.

1. **Write down the costs:**
- Cost of milk = Rs. 1.80
- Cost of water = Rs. 0.00
- Cost of mixture = Rs. 0.90

2. **Calculate the differences:**
- Difference between the cost of milk and the cost of the mixture:
\[ 1.80 - 0.90 = 0.90 \]
- Difference between the cost of water and the cost of the mixture:
\[ 0.90 - 0.00 = 0.90 \]

### Step 3: Set up the ratio
According to the alligation rule, the ratio of the quantities of milk and water can be determined by the differences calculated above.

- The ratio of milk to water is:
\[ \text{Milk : Water} = 0.90 : 0.90 = 1 : 1 \]

### Step 4: Calculate the quantity of milk
Since the quantity of water is given as 16 litres, we can use the ratio to find the quantity of milk.

1. **Let the quantity of milk be \( x \) litres.**
2. From the ratio \( 1 : 1 \), we have:
\[ \frac{x}{16} = \frac{1}{1} \]
This implies that \( x = 16 \) litres.

### Conclusion
Thus, the quantity of milk in the mixture is **16 litres**.

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