The center of mass is defined to be the point where the torques due to the various components of weight of an object = 0. Remember torque = force (in this case weight) times moment arm distance. Let's call the location of the CM as being distance D as measured from point Y. There are two moment armsacting about the CM to consider: the one acting at point Y has a force of 800N and has a moment arm length from the CM of D, so the torque this force presents at point D is Dx800N in the clockwise direction. The torque due to the 700N load at point X has a moment arm length of (LD), so presents a torque to point D of 700(LX) in the counterclockwise direction. By convention counterclockwise torques are considered positive and clockwise is negative. The sum of these two torques acting about point D must equal zero (that's the definition of the center of mass):
$\displaystyle \sum T = 700(LX)800X = 0$
Solve for X.
As for question 13  it doesn't matter whether you weigh both ends of the bed at the same time or not  it's static, and so its weight doesn't change, and neither does the center of mass. Hence you get the same readings whether you use two scales on one.
