Method 1
$1$ feet = $12$ inches
So $5$ feet $5$ inches = $65$ inches.
So $65$ inches is the actual height of the candidate.
Height which he wrote on certificate = $65$ + ($25\%$ of $65$) = $65+16.25 = 81.25$ inches.
So $Percentage\ correction$
$= \frac{Wrong\ height - Actual\ Height}{Actual\ height} * 100 $
$= \frac{81.25 - 65}{65} *100 $
$= \frac{16.25}{65} *100 $
$= 25\% $
Method 2
the original height was $5$ feet $5$ inches
But he increased his height by $25\%$ and wrote in the certificate.
So what will he do to make it correct ?
Decrease the height by $25\%$ which is written in the certificate.
So option 3. $25$ is correct answer.