In a mixture of 60L the ratio of acid and water is `2 : 1`.If the ratio of acid and water is to be `1 : 2`, then the amount of water(in litre) to be added to the mixture is

Options

A. 55
B. 60
C. 50
D. 45

Answer

To solve the problem, we need to determine how much water needs to be added to change the ratio of acid to water in a 60-liter mixture from 2:1 to 1:2.

### Step-by-Step Solution:

1. **Determine the current amounts of acid and water in the mixture:**
- The total volume of the mixture is 60 liters.
- The ratio of acid to water is 2:1. This means for every 2 parts of acid, there is 1 part of water.
- Let the amount of acid be \(2x\) and the amount of water be \(x\).
- Therefore, \(2x + x = 60\).
- This simplifies to \(3x = 60\).
- Solving for \(x\), we find \(x = 20\).
- Thus, the amount of acid is \(2x = 40\) liters and the amount of water is \(x = 20\) liters.

2. **Set up the new ratio of acid to water:**
- We want the new ratio of acid to water to be 1:2.
- Let the amount of water to be added be \(y\) liters.
- The new amount of water will then be \(20 + y\) liters.
- The amount of acid remains the same at 40 liters.

3. **Formulate the equation based on the new ratio:**
- According to the new ratio, we have:
\[ \frac{\text{Acid}}{\text{Water}} = \frac{1}{2} \]
- This translates to:
\[ \frac{40}{20 + y} = \frac{1}{2} \]

4. **Cross-multiply to solve for \(y\):**
- Cross-multiplying gives:
\[ 40 \cdot 2 = 1 \cdot (20 + y) \]
- This simplifies to:
\[ 80 = 20 + y \]
- Rearranging gives:
\[ y = 80 - 20 = 60 \]

5. **Conclusion:**
- Therefore, the amount of water to be added to the mixture is **60 liters**.