In a metre-bridge when a resistance in the left gap is 2 Ω and unknown resistance in the right gap, the…

In first circuit:

For balanced condition, we get $\frac{2}{40}=\frac{X}{60}\Rightarrow X=3\Omega$

In second case:

Net resistance of the right side due to shunting becomes,  ${\mathrm{X}}^{\text{'}}=\frac{2\times 3}{2+3}=1.2 \Omega$

Again for balanced condition, 

$\frac{2}{\ell }=\frac{1.2}{100-\ell }$

$\Rightarrow 200-2\ell =1.2\ell$

$\Rightarrow \mathrm{\ell }=\frac{200}{3.2}=62.5 \mathrm{cm}$

Clearly, balance length changes by $22.5 \mathrm{cm}$.