In a 25 litre mixture of milk and water, the water is only 20%. How many litres of water is required to increase the percentage of water to 90%?

Options

A. 45 litre
B. 70 litre
C. 115 litre
D. 175 litre

Answer

To solve the problem step by step, we will break down the question and find out how much water is needed to increase the percentage of water in the mixture to 90%.

### Step 1: Determine the initial amounts of water and milk in the mixture.
The total volume of the mixture is 25 liters, and the water constitutes 20% of this mixture.

\[ \text{Amount of water} = 20\% \text{ of } 25 \text{ liters} = \frac{20}{100} \times 25 = 5 \text{ liters} \]

\[ \text{Amount of milk} = \text{Total mixture} - \text{Amount of water} = 25 - 5 = 20 \text{ liters} \]

### Step 2: Set up the equation for the new mixture.
We want to increase the percentage of water to 90%. Let \( x \) be the amount of water we need to add. After adding \( x \) liters of water, the new amount of water will be \( 5 + x \) liters, and the amount of milk will remain 20 liters.

The total volume of the new mixture will be:

\[ \text{Total mixture} = 25 + x \text{ liters} \]

### Step 3: Set up the equation for the new percentage of water.
We want the percentage of water in the new mixture to be 90%. Therefore, we can set up the equation:

\[ \frac{5 + x}{25 + x} = 90\% \]

Converting 90% to a fraction gives us:

\[ \frac{90}{100} = \frac{9}{10} \]

### Step 4: Cross-multiply to solve for \( x \).
Now we can cross-multiply:

\[ 10(5 + x) = 9(25 + x) \]

Expanding both sides:

\[ 50 + 10x = 225 + 9x \]

### Step 5: Rearrange the equation to isolate \( x \).
Now, we can rearrange the equation:

\[ 10x - 9x = 225 - 50 \]

\[ x = 175 \]

### Conclusion
Thus, the amount of water required to increase the percentage of water to 90% is **175 liters**.

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