Given:
- The water tank is currently 2/5 th full.
- Pipe A can fill the tank in 10 minutes.
- Pipe B can empty the tank in 6 minutes.

To find:
- How long will it take to empty or fill the tank completely if both pipes A and B are open?

Solution:

To find the time required to empty or fill the tank completely, we need to consider the rate at which water is being filled and emptied by both pipes.

Let's first find the rates of filling and emptying:
- Pipe A can fill the tank in 10 minutes, so its rate of filling is 1/10 th of the tank per minute.
- Pipe B can empty the tank in 6 minutes, so its rate of emptying is 1/6 th of the tank per minute.

Step 1: Determine the rate of filling or emptying when both pipes are open.

Since pipe A is filling the tank and pipe B is emptying it, we need to find the net rate of filling or emptying when both pipes are open.

The net rate can be calculated by subtracting the rate of emptying from the rate of filling:
Net rate = Rate of filling - Rate of emptying

Net rate = 1/10 - 1/6

Simplifying, we get:
Net rate = (3 - 5)/30
Net rate = -2/30
Net rate = -1/15

Step 2: Determine the time required to empty or fill the tank completely.

Since the net rate is negative, it means the tank is being emptied.

To find the time required to empty the tank completely, we can use the formula:
Time = Capacity / Rate

Since the tank is 2/5 th full, its capacity is 2/5.

Using the formula, we get:
Time = (2/5) / (1/15)

Simplifying, we get:
Time = (2/5) * (15/1)
Time = 6

Therefore, it will take 6 minutes to empty the tank completely when both pipes A and B are open.

Conclusion:
- When both pipes A and B are open, it will take 6 minutes to empty the tank completely.