Let $X$ and $Y$ represents $31$ and $- 31$ respectively in binary sign magnitude form. $X$ and $Y$ will take $6$ bits as range of sign magnitude form is $-\left(2^{(n-1)}-1\right)$ to $2^{(n-1)}-1$; where $n$ is the number of bits.
Now in question $Z= X-Y$,
$Z = 31 - (-31) = 62$
To represent $62$ in sign magnitude form we need $7\;( 6+1)$ bits.
Hence, $n+1$ bits needed.
Answer is $C$.