Population of a town increased by $1200$ persons in a year and then this new population decreased by $11\%$ during the next year. If the town now has $32$ persons less than it had before the increase, then the original population of the town is:

The correct option is A. $10000$
Let $x$ be the original population,
Population increased by $1200$,
hence, new population is $1200+x$
Now, the population decreased by $11\%$, now population is
$=(1200+x)-\frac{11}{100}(1200+x)$
Also, population $=x-32$

Thus, $(1200+x)-\frac{11}{100}(1200+x)=x-32$
$\Rightarrow (1-\frac{11}{100})(1200+x)=x-32$
$\Rightarrow \frac{89}{100}(1200+x)=x-32$
$\Rightarrow 89(1200+x)=100(x-32)$
$\Rightarrow 106800+89x=100x-3200$
$\Rightarrow 100x-89x=106800+3200$
$\Rightarrow 11x=110000$
$\Rightarrow x=\frac{110000}{11}$
$\Rightarrow x=10,000$

Hence, option 'B' is correct.