Given that the first installment is $Rs.100$

Each installment is increased by $Rs.5$

$\therefore$ The amount repaid by the man in each month is given by

$100,105,110,115,...........$ respectively.

This sequence is A.P. with first term $=a=100$ and common difference $=d=5$

The $30^{th}$ installment=$30^{th}$ term in this sequence.

We know that $n^{th}$ term of an A.P.=$t_n=a+(n-1)d$

$i.e., t_{30}=a+(30-1)d=100+29\times 5=245$

$\therefore$ The amount paid by the man in the $30^{th}$ installment=$Rs.245$