A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected cross the other gap. When these resistance are interchanged, the balance point shifts by 20cm. Neglecting any corrections, what is the unknown resistance?

3Ω

$\text{From first condition } \frac{R}{x} = \frac{l}{100-l}$

$\text{From second condition } \frac{x}{R} = \frac{l+20}{80-l}$

$\text{Solving } l = 40cm$

$\Rightarrow x = 3\Omega$