Let x be the total amount of money Bill and Ben won.

We know that the ratio of Ben's money to Bill's money is 3:4, so:

3/4 = x / (x-400)

We also know that the ratio of Ben's money (after giving P400 to his sister) to Bill's money is 6:7, so:

6/7 = (x-400) / x

We can use these two equations to solve for x.

First, cross-multiply the first equation:

4x = 3(x-400)

Then, cross-multiply the second equation:

7(x-400) = 6x

Now we can substitute the first equation into the second equation:

7(4x/3) = 6x

Simplifying this equation:

8x = 21x - 2800

13x = 2800

x = 21600

Therefore, the total amount of money Bill and Ben won is P21600.