Consider thin uniform rod $AB$ of mass $m$ and length $L$ just translating with some acceleration $a$ due to two anti parallel forces $F_1$ and $F_2$ perpendicular to the rod. Force $F_1$ acts at the end $A$ where as $F_2$ acts at distance $y$ from end $A$.
Because body is just translating, Net torque on the body about any point on the rod be zero.
About Center of Mass:
$F_1.L/2 = F_2.(L/2-y)$ gives me a ratio of $F1/F2$
If I proceed with these values of F1 and F2 then net torque about the end B is not zero.
About end B of the rod:
$F_1.L = F_2.(L-y)$ gives me another value for $F1/F2$
If I proceed with these values of F1 and F2 then net torque about the center of mass is not zero.
Where am I going wrong?
EDIT: I have generalized the above situation from the following problem:
Solution to the above problem says "Since the rod moves translationally only, Hence Torque about $B$ is zero. Hence $N = 0$ and hence $x=2$"