Three children are standing on a 5 × 5-m raft. The weights of the children at points A, B, and C are 375 N, 260 N, and 400 N, respectively. If a fourth child of weight 425 N climbs onto the raft, determine where she should stand if the other children remain in the positions shown and the line of action of the resultant of the four weights is to pass through the center of the raft.
Fig. P3.96

Given that,
Position of first child, 
Weight of the child at A, 
Position of second child, 
Weight of the child at B, 
Position of third child, 
Weight of the child at C, 
Weight of the fourth child at D, 
Let Position of fourth child, 
Also given that the resultant of the four weights is acting at the center of the raft i.e., at 
We have, 
Take moment about x-axis.
Therefore, the distance is
from edge OE
Take moment about z-axis.
Therefore, the distance is
from edge OG