Metal wire is connected in the left gap, Germanium connected in the right gap of metre bridge and balancing point is found at 50 cm. Metal wire is heated and Germanium is cooled so that variations of resistances in them are equal. Then the balancing point

Initially balance point is at 50cm, which means the resistance of the metal wire and germanium is same. 

After heating the wire and cooling germanium, given that the variation in resistance is same for both. Since the initial resistances and the variations are equal, the final resistances will also be equal.

For equal resistances, the balance point will be at 50cm only with no change.