Explanation:

Certainly! Let's break down the problem:

- Initial Mixture: The mixture is 90 liters and consists of 20% water.

- Calculation: 20% of 90 liters is 18 liters of water. So, there are 18 liters of water and 72 liters of spirit initially.

- Goal: We want water to be 50% of the new mixture.

To achieve this:

- Let the amount of water to be added be 'x' liters.

- The total water will then be \(18 + x\) liters.

- The new total mixture will become \(90 + x\) liters.

For water to be 50%:

$$

\frac{18 + x}{90 + x} = 0.5

$$

Solving this equation:

1. Multiply both sides by \(90 + x\):

$$

18 + x = 0.5 \times (90 + x)

$$

2. Simplify:

$$

18 + x = 45 + 0.5x

$$

3. Rearrange and solve for \(x\):

$$

18 + 0.5x = 45 \Rightarrow 0.5x = 27 \Rightarrow x = 54

$$

Option 3: 54 liters is indeed the correct amount of water to be added.

- Option 1: 50 liters: This would lead to less than 50% water.

- Option 2: 60 liters: This would result in more than 50% water.

- Option 4: 70 liters: Would also result in more than 50% water.

- Option 5: None of these: Incorrect as option 3 works.

Correct Answer: Option 3: 54 liters