A mixture of 30 litres of spirit and water contains 20% of water in it. How much water must be added to it, to make the water 25% in the new mixture ?

Options

A. 3 litres
B. 2 litres
C. 4 litres
D. None of these

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the amount of water in the initial mixture.
The mixture is 30 liters and contains 20% water.

\[ \text{Amount of water} = 20\% \text{ of } 30 \text{ liters} = \frac{20}{100} \times 30 = 6 \text{ liters} \]

### Step 2: Determine the amount of spirit in the initial mixture.
Since the total mixture is 30 liters and we have found that there are 6 liters of water, we can find the amount of spirit.

\[ \text{Amount of spirit} = 30 \text{ liters} - \text{Amount of water} = 30 - 6 = 24 \text{ liters} \]

### Step 3: 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 total volume of the mixture will be \( 30 + x \) liters. The total amount of water will then be \( 6 + x \) liters.

We want the new mixture to have 25% water. Therefore, we can set up the equation:

\[ \frac{6 + x}{30 + x} = \frac{25}{100} \]

### Step 4: Cross-multiply to eliminate the fraction.
Cross-multiplying gives us:

\[ 100(6 + x) = 25(30 + x) \]

### Step 5: Simplify the equation.
Expanding both sides:

\[ 600 + 100x = 750 + 25x \]

### Step 6: Rearrange the equation to isolate \( x \).
Bringing all terms involving \( x \) to one side and constant terms to the other side:

\[ 100x - 25x = 750 - 600 \]

This simplifies to:

\[ 75x = 150 \]

### Step 7: Solve for \( x \).
Dividing both sides by 75:

\[ x = \frac{150}{75} = 2 \]

### Conclusion:
Thus, the amount of water that must be added to the mixture to make the water 25% in the new mixture is **2 liters**.

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