CEMC Pascal, 1998

Three rugs have a combined area of $200\,\text{m}^2$. By overlapping the rugs to cover a floor area of $140\,\text{m}^2$, the area which is covered by exactly two layers of rug is $24\,\text{m}^2$. What area of floor is covered by three layers of rug?

(A) $12\,\text{m}^2$ (B) $18\,\text{m}^2$ (C) $24\,\text{m}^2$ (D) $36\,\text{m}^2$ (E) $42\,\text{m}^2$