The ends of a metre stick are maintained at 100°C and 0°C. One end of a rod is maintained at 25°C. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?

Let the point to be touched be ‘B’
No heat will flow when, the temp at that point is also 25°C
i.e. Q_AB = Q_BC

So, (KA(100 - 25)/(100 - x) = (KA(25 - 0)/x

=> 75x = 2500 – 25x => 100x = 2500 => x = 25cm from the end with 0°C