Equality on ratio of infimum of measures

Question

Let $(\mathcal X,\Sigma_X)$ be a measurable space, let $p$ and $q$ be two probability measures on $(\mathcal X,\Sigma_X)$ and let $f:\mathcal X\to[0,\infty[$ be a measurable function such that $q(f)$ and $p(f)$ are finite and $f>0$ $q$-almost surely. I want to show the following equality (or determine under which aditional assumption it is true) \begin{align*} \inf_{\substack{B\in\Sigma_X:\\q(1_B \cdot f)>0}} \frac{p(1_B\cdot f)}{q(1_B\cdot f)}=\inf_{\substack{B\in \Sigma_X:\\q(B)>0}}\frac{p(B)}{q(B)} \end{align*} I'm not even sure how to start with this one.