40 litres of 60% concentration of acid solution is added to 35 litres of 80% concentration of acid solution. What is the concentration of acid in the new solution ?

Options

A. `66%`
B. `66(2)/(3)%`
C. `69(1)/(3)%`
D. `69%`

Answer

To find the concentration of acid in the new solution formed by mixing two acid solutions, we can follow these steps:

### Step 1: Calculate the amount of acid in the first solution
The first solution has a volume of 40 liters with a concentration of 60%.

\[ \text{Amount of acid in the first solution} = \text{Volume} \times \text{Concentration} = 40 \, \text{liters} \times 0.60 = 24 \, \text{liters} \]

### Step 2: Calculate the amount of acid in the second solution
The second solution has a volume of 35 liters with a concentration of 80%.

\[ \text{Amount of acid in the second solution} = \text{Volume} \times \text{Concentration} = 35 \, \text{liters} \times 0.80 = 28 \, \text{liters} \]

### Step 3: Calculate the total amount of acid in the new solution
Now, we add the amounts of acid from both solutions:

\[ \text{Total amount of acid} = \text{Amount from first solution} + \text{Amount from second solution} = 24 \, \text{liters} + 28 \, \text{liters} = 52 \, \text{liters} \]

### Step 4: Calculate the total volume of the new solution
The total volume of the new solution is the sum of the volumes of both solutions:

\[ \text{Total volume} = 40 \, \text{liters} + 35 \, \text{liters} = 75 \, \text{liters} \]

### Step 5: Calculate the concentration of acid in the new solution
The concentration of acid in the new solution can be calculated using the formula:

\[ \text{Concentration} = \left( \frac{\text{Total amount of acid}}{\text{Total volume}} \right) \times 100 \]

Substituting the values we calculated:

\[ \text{Concentration} = \left( \frac{52 \, \text{liters}}{75 \, \text{liters}} \right) \times 100 \]

Calculating this gives:

\[ \text{Concentration} = \left( \frac{52}{75} \right) \times 100 = 69.33\% \]

### Final Answer:
The concentration of acid in the new solution is approximately **69.33%**.

---