Very hard hanging rod problem

Question

A straight rod of 30 cm and 600 g mass is horizontally hanged on two upright, parallel and light threads, both of them attached with distances of 5 cm and 10 cm from its ends. Find tension forces of the threads and distance (in milimeters) from rod's centre of mass to the point where you need to hang additional load of 400 g so that tension forces of the threads become equal. How the forces changed after hanging the load? Strenght of gravitational field is 9,8 N/kg

I'd really appreciate if you provide a detailed explanation on solving this problem.

Answer 1

The 400g mass should be located at 9 cm

Answer 2