UKMT Senior Mathematical Challenge, 2022

Three rugs have a combined area of $90\,\mathrm{m}^2$. When they are laid down to cover completely a floor of area $60\,\mathrm{m}^2$, the area which is covered by exactly two layers of rug is $12\,\mathrm{m}^2$. What is the area of floor covered by exactly three layers of rug?

(A) $2\,\mathrm{m}^2$ (B) $6\,\mathrm{m}^2$ (C) $9\,\mathrm{m}^2$ (D) $10\,\mathrm{m}^2$ (E) $12\,\mathrm{m}^2$