A stick is supported at the centre, and a block of 5kg is hung at the 80-cm mark. Another block is added to balance the system when it is hung at the 10-cm mark. What is the weight of the second block?

well, summing moments about the center. C is the center point.

(80-C)5-(C-10)W=0
would be very easy to solve forthe weight W if we know where the center was.