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, let's break it down clearly:

### Step 1: Determine the initial quantities of milk and water in the mixture.
Given that the total mixture is 25 liters and water constitutes 20% of it:
- Water = 20% of 25 liters = \( \frac{20}{100} \times 25 = 5 \) liters
- Milk = 80% of 25 liters = \( \frac{80}{100} \times 25 = 20 \) liters

### Step 2: Set up the new scenario after adding water.
We want to increase the percentage of water to 90%. This means that in the new mixture, water will be 90% and milk will be 10%. Let \( x \) be the amount of water we need to add.

After adding \( x \) liters of water, the new total volume of the mixture will be:
- New total volume = \( 25 + x \) liters

### Step 3: Set up the equation based on the new percentage of water.
In the new mixture, the amount of water will be:
- New amount of water = \( 5 + x \) liters

We want this to be 90% of the new total volume:
\[ 5 + x = 90\% \text{ of } (25 + x) \]
This can be expressed mathematically as:
\[ 5 + x = \frac{90}{100} \times (25 + x) \]

### Step 4: Solve the equation.
First, simplify the right side:
\[ 5 + x = 0.9 \times (25 + x) \]
\[ 5 + x = 22.5 + 0.9x \]

Now, isolate \( x \):
\[ 5 + x - 0.9x = 22.5 \]
\[ 5 + 0.1x = 22.5 \]
\[ 0.1x = 22.5 - 5 \]
\[ 0.1x = 17.5 \]
\[ x = \frac{17.5}{0.1} = 175 \]

### Step 5: Conclusion
The amount of water required to increase the percentage of water to 90% is **175 liters**.

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