I think there should be 22 steps. What do think?
This is how I worked it out:
I had climbed down seven steps when the boy starts.
After that I climb down a further number of steps (let this number be "x") when the boy reaches the top.
I have yet to climb down four more stairs.
Therefore, the total number of stairs is: 7 + x + 4, or 11 + x.
The boy takes two steps at a time. So when I have taken "x" steps, he has climbed up 2x number of steps and reached the top. Therefore, the total number of steps is 2x.
Thus, 11 + x = 2x.
Thus, x = 11.
The total number of steps is 2x. Substitute x = 11, and we have the total number of steps as 22.