An 80 litre mixture of water and acid contains 20% acid. How much acid should be added to make the acid 60% in the new mixture?

Options

A. 60
B. 80
C. 70
D. 90

Answer

To solve the problem step by step, we need to determine how much acid should be added to an 80-liter mixture that currently contains 20% acid in order to make the acid concentration 60%.

### Step 1: Determine the initial amount of acid in the mixture.
The initial mixture is 80 liters and contains 20% acid.

\[ \text{Amount of acid} = 20\% \text{ of } 80 \text{ liters} = \frac{20}{100} \times 80 = 16 \text{ liters} \]

### Step 2: Determine the initial amount of water in the mixture.
Since the mixture is made up of acid and water, the amount of water can be calculated as:

\[ \text{Amount of water} = 80 \text{ liters} - 16 \text{ liters} = 64 \text{ liters} \]

### Step 3: Set up the equation for the new mixture.
Let \( x \) be the amount of acid to be added. After adding \( x \) liters of acid, the new amount of acid will be:

\[ \text{New amount of acid} = 16 + x \text{ liters} \]

The total volume of the new mixture will be:

\[ \text{Total volume} = 80 \text{ liters} + x \text{ liters} \]

### Step 4: Set up the equation for the percentage of acid in the new mixture.
We want the new mixture to contain 60% acid. Therefore, we can set up the equation:

\[ \frac{16 + x}{80 + x} = 0.6 \]

### Step 5: Solve the equation for \( x \).
Cross-multiplying gives:

\[ 16 + x = 0.6(80 + x) \]

Expanding the right side:

\[ 16 + x = 48 + 0.6x \]

Now, isolate \( x \):

\[ 16 + x - 0.6x = 48 \]

\[ 16 + 0.4x = 48 \]

Subtract 16 from both sides:

\[ 0.4x = 32 \]

Now divide by 0.4:

\[ x = \frac{32}{0.4} = 80 \text{ liters} \]

### Conclusion:
The amount of acid that should be added to make the acid concentration 60% in the new mixture is **80 liters**.