A mixture of 240 litres of juice and water contains 15% water. How much more water (in litres) should be added to this so that the strength of water will become 25% in the new mixture?

Options

A. 28
B. 32
C. 26
D. 34

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the initial amount of water in the mixture.
The total volume of the mixture is 240 liters, and it contains 15% water.

\[ \text{Amount of water} = \frac{15}{100} \times 240 = 36 \text{ liters} \]

### Step 2: Set up the equation for the new mixture.
Let \( x \) be the amount of water to be added. After adding \( x \) liters of water, the new amount of water will be:

\[ \text{New amount of water} = 36 + x \text{ liters} \]

The total volume of the mixture after adding \( x \) liters of water will be:

\[ \text{Total volume} = 240 + x \text{ liters} \]

### Step 3: Set up the equation for the percentage of water in the new mixture.
We want the strength of water in the new mixture to be 25%. Therefore, we can set up the equation:

\[ \frac{36 + x}{240 + x} = \frac{25}{100} = \frac{1}{4} \]

### Step 4: Cross-multiply to solve for \( x \).
Cross-multiplying gives us:

\[ 4(36 + x) = 1(240 + x) \]

Expanding both sides:

\[ 144 + 4x = 240 + x \]

### Step 5: Rearrange the equation to isolate \( x \).
Now, we will move all terms involving \( x \) to one side and constant terms to the other side:

\[ 4x - x = 240 - 144 \]

This simplifies to:

\[ 3x = 96 \]

### Step 6: Solve for \( x \).
Dividing both sides by 3 gives:

\[ x = \frac{96}{3} = 32 \]

### Conclusion
The amount of water that should be added to the mixture is **32 liters**.

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