The resistance per centimeter of a meter bridge wire is r , with XΩ...

For first case:

$\dfrac{X}{r{l}_{1}} = \dfrac{25}{r{l}_{2}}$ ... (i)

For second case:

$\dfrac{X}{\left(2r\right){l}^{'}1}$ = \dfrac{25}{\left(2r\right)l{'}_{2}} ... (ii)

From (i) and (ii), we get

$\dfrac{l{'}_{1}}{{l}_{1}} = \dfrac{l{'}_{2}}{{l}_{2}}$ also total length is constant.

Therefore, balance length doesn't change and 

$l{'}_{1} = {l}_{1} = 40cm$