30 litres of salt solution contains 1.5 l salt. How many litres of water must be added so as to get a resultant solution containing 3% salt?

Options

A. A. 20
B. B. 30
C. C.10
D. D. 40

Answer

To solve the problem step by step, we need to determine how many liters of water must be added to a salt solution to achieve a desired concentration of salt.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have a total of 30 liters of salt solution.
- The amount of salt in this solution is 1.5 liters.

2. **Define the Variable**:
- Let \( x \) be the amount of water (in liters) that we need to add to the solution.

3. **Set Up the Equation**:
- After adding \( x \) liters of water, the total volume of the solution will be \( 30 + x \) liters.
- The amount of salt remains the same at 1.5 liters.
- We want the final solution to contain 3% salt. This can be expressed as:
\[ \frac{\text{Amount of salt}}{\text{Total solution}} = \frac{1.5}{30 + x} = 0.03 \]

4. **Cross Multiply to Solve for \( x \)**:
- Rearranging the equation gives:
\[ 1.5 = 0.03 \times (30 + x) \]
- Expanding the right side:
\[ 1.5 = 0.9 + 0.03x \]

5. **Isolate \( x \)**:
- Subtract 0.9 from both sides:
\[ 1.5 - 0.9 = 0.03x \]
\[ 0.6 = 0.03x \]
- Now, divide both sides by 0.03 to find \( x \):
\[ x = \frac{0.6}{0.03} = 20 \]

6. **Conclusion**:
- Therefore, the amount of water that must be added is \( 20 \) liters.

### Final Answer:
20 liters of water must be added to achieve a solution containing 3% salt.

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