Fig. (a) $\quad$ Fig. (b)
Given that $\mathrm{Y}=12.5 \Omega, l_1=39.5 \mathrm{~cm}$, $\ell_2=100-39.5=60.5 \mathrm{~cm}, \mathrm{X}=$ ?
By formula, $\frac{\mathrm{X}}{\mathrm{Y}}=\frac{\ell_1}{\ell_2}$ and
$$
\mathrm{X}=\mathrm{Y} \frac{\ell_1}{\ell_2}=\frac{12.5 \times 39.5}{60.5}=8.1612 \Omega \text {. }
$$
Thick copper strips are used for connections to minimise resistance of connection which are not accounted for in bridge formula.
(b) When $\mathrm{X}$ and $\mathrm{Y}$ are interchanged, values of $\ell_1$ and $\ell_2$ also become interchanged. Then $\ell_1=60.5 \mathrm{~cm}$. Hence balance point will be at $60.5 \mathrm{~cm}$.
(c) When galvanometer and cell are interchanged, condition for balance of bridge remains satisfied. Hence galvanometer will not show any current.