M1 Moments hard question

I have posted the question and solution. What I would like to know is how I am meant to know that the support is meant to sit between the broom head and the brooms centre of mass. Logically it makes sense to put it there so that the broom balances but in terms of the question there is nothing to suggest that it goes there. After all if it were on the other end of the stick then you could no longer use (0.65 - xm) as the distance to the pivot and the solution obtained would be wrong.

Using the principle of moments and with the given forces, you see immediately that for the object to be in equilibrium, there must be a force acting either side of the support.

Thank you