Explanation:

Let’s break it down:

- The mixture is first in ratio A:B = 7:5.

- Let the total volume be x liters. So, A = (7/12)x and B = (5/12)x.

- You remove 9 liters of the mixture. That’s 9*(7/12) = 5.25 liters A and 9*(5/12) = 3.75 liters B.

- You add back 9 liters of B.

- After this, you have: A = (7/12)x – 5.25; B = (5/12)x – 3.75 + 9.

- New ratio: (A) : (B) = 7 : 9.

So, set up the equation:

[(7/12)x – 5.25] / [(5/12)x – 3.75 + 9] = 7/9

- Cross-multiplying: 9[(7/12)x – 5.25] = 7[(5/12)x + 5.25]

- Distribute: (21/4)x – 47.25 = (35/12)x + 36.75

- Get all x on one side: (21/4)x – (35/12)x = 36.75 + 47.25

- LCM of 4 and 12 is 12, so: (63/12)x – (35/12)x = 84

- (28/12)x = 84 ? (7/3)x = 84 ? x = 84 * 3 / 7 = 36

- Initial A = (7/12)x = (7/12)*36 = 21

So, here’s how the options play out:

1. 21 liters ? This is correct.

2. 35 liters (that’s if x?=?60, which doesn’t fit the ratios and process)

3. 40 liters (similarly, doesn’t match the equations)

4. 19 liters (again, doesn’t satisfy the ratio or process)