A 100 ml solution contain `80%` of basic acid. How much water should be added to this solution to make it a solution with `50%` of basic acid ?

Options

A. `60` ml
B. `70` ml
C. `80` ml
D. `65` ml

Answer

To solve the problem of how much water should be added to a 100 ml solution containing 80% basic acid to make it a 50% basic acid solution, follow these steps:

### Step-by-Step Solution:

1. **Determine the amount of basic acid in the original solution:**
- The original solution is 100 ml and contains 80% basic acid.
- Amount of basic acid = 80% of 100 ml = (80/100) * 100 ml = 80 ml.

2. **Determine the amount of water in the original solution:**
- Since the solution is 100 ml and contains 80 ml of basic acid, the remaining volume is water.
- Amount of water = Total volume - Amount of basic acid = 100 ml - 80 ml = 20 ml.

3. **Set up the equation for the final solution:**
- Let \( x \) be the amount of water to be added.
- The new total volume of the solution after adding water will be \( 100 ml + x \).
- The amount of basic acid remains the same at 80 ml.

4. **Express the new concentration of basic acid:**
- We want the new solution to be 50% basic acid.
- Therefore, the equation for the concentration is:
\[ \frac{80 \text{ ml}}{100 \text{ ml} + x} = 50\% \]
- This can be rewritten as:
\[ \frac{80}{100 + x} = \frac{50}{100} \]

5. **Cross-multiply to solve for \( x \):**
- Cross-multiplying gives:
\[ 80 \times 100 = 50 \times (100 + x) \]
- This simplifies to:
\[ 8000 = 5000 + 50x \]

6. **Isolate \( x \):**
- Subtract 5000 from both sides:
\[ 8000 - 5000 = 50x \]
\[ 3000 = 50x \]
- Divide both sides by 50:
\[ x = \frac{3000}{50} = 60 \]

7. **Conclusion:**
- Therefore, the amount of water that should be added is **60 ml**.