Uniform rod of weight 10N and length 5m is supported by ropes from points P and Q. The rope at P is attached 1.0m from end M and the rope at Q is attached 0.25m from end O. find the tensions Tp and Tq

Answer 1

Set the moment about point P equal to zero and solve for Tq, and then..
Set the moment about point Q equal to zero and solve for Tp.

Remember that the weight of the rod acts as if it were applied at its center of mass.

Tp + Tq = 10 N if you do it right.

Answer 2

Tp=6N
Tq=4