A 20 ohm resistor is connected in left gap and an unknown resistance is in right gap of meter bridge. Also,the null deflection point is shifted by 40cm when resistors are interchanged.find value of unknown resistance

in the first case the deflection point is taken as L1. Let the balance point gets shifted to L2 by 40 cm when the resistors are interchanged.

So we get L1 - L2 = 40

Also we know L1 + L2 = 100

Solving these two equations we get ,L2 = 30 cm and L1 = 70 cm.