Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. Then

Since, number of subsets of a set containing m elements is 112 more than the subsets of the set containing n elements. $2^m-2^n=112$$\Rightarrow 2^n.\left(2^{m-n}-1\right)=2^4.7$$\Rightarrow 2^n=2^4$ and  $2^{m-n}-1=7$$\Rightarrow n=4$  and  $2^{m-n}=8$ $\Rightarrow 2^{m-n}=2^3\Rightarrow m-n=3$$\Rightarrow m-4=3\Rightarrow m=4+3$

$\Rightarrow m=7$.