What is the quantity of milk in a mixture of milk and water?

Statement I: If 10 liters of the mixture is removed, then water constitutes 35\% of the total quantity of the remaining mixture.

Statement II: If 30 liters of water is added to the initial mixture, then the quantity of milk becomes equal to the quantity of water.

Question

What is the quantity of milk in a mixture of milk and water?

Statement I: If 10 liters of the mixture is removed, then water constitutes 35\% of the total quantity of the remaining mixture.

Statement II: If 30 liters of water is added to the initial mixture, then the quantity of milk becomes equal to the quantity of water.

Accepted Answer

**Solution:**

Let the quantity of milk be *M* liters and water be *W* liters in the initial mixture.

**From Statement I:**
- When 10 liters of mixture is taken out, the ratio of milk to water remains the same.
- The quantity of mixture left = (M + W) - 10 liters.
- Water becomes 35\% of the remaining mixture:
  $$\frac{W - 10 	imes \frac{W}{M+W}}{M + W - 10} = 0.35$$
- This gives one equation involving *M* and *W*.

**From Statement II:**
- Adding 30 liters of water makes milk equal to water:
  $$M = W + 30$$
- This is a second equation relating *M* and *W*.

**Analysis:**
- Statement I alone gives one equation with two variables, insufficient to find *M*.
- Statement II alone also gives one equation with two variables, insufficient to find *M*.
- Combining both statements, we get two equations with two variables, which can be solved to find the exact quantity of milk.

**Answer:** Both statements together are necessary to determine the quantity of milk.

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