UKMT Intermediate Mathematical Challenge, 2023

A rectangle $PQRS$ has side-lengths $a$ and $b$, with $a < b$. The rectangle $PTUV$ has side-lengths $c$ and $d$, with $c < d$. Also, $a < d$ and $c < b$, as shown. The sides $RS$ and $TU$ cross at $X$. Which of these conditions guarantees that $Q$, $X$ and $V$ lie on a straight line?

(A) $\dfrac{a}{b}+\dfrac{c}{d}=1$ (B) $\dfrac{a}{c}+\dfrac{b}{d}=1$ (C) $\dfrac{a}{d}+\dfrac{c}{b}=1$ (D) $\dfrac{a}{c}+\dfrac{d}{b}=1$ (E) $\dfrac{c}{a}+\dfrac{b}{d}=1$