We can solve the problem by requiring the equilibrium of the forces and the equilibrium of torques.
1) Equilibrium of forces:
[tex]T_1 - W_p - W_s + T_2 =0[/tex]
where
[tex]W_p = (90kg)(9.81 m/s^2)=883 N[/tex] is the weight of the person
[tex]W_s = (200kg)(9.81 m/s^2)=1962 N[/tex] is the weight of the scaffold
Re-arranging, we can write the equation as
[tex]T_1 = 2845 N-T_2[/tex] (1)
2) Equilibrium of torques:
[tex] T_1 \cdot 3 m - W_p \cdot 2 m - T_2 \cdot 3m =0[/tex]
where 3 m and 2 m are the distances of the forces from the center of mass of the scaffold.
Using [tex]W_p = 883 N[/tex] and replacing T1 with (1), we find
[tex]2845 N \cdot 3 m - T_2 \cdot 3 m - 833 N \cdot 2 m - T_2 \cdot 3 m=0[/tex]
from which we find
[tex]T_2 = 1128 N[/tex]
And then, substituting T2 into (1), we find
[tex]T_1 = 1717 N[/tex]
