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Algebra Difficulty 2.0 Junior Find the answer Canada

The two whole numbers $m$ and $n$ satisfy $m+n=20$ and $\frac{1}{m}+\frac{1}{n}=\frac{5}{24}$ . The product $mn$ is equal to

(A) $72$ (B) $36$ (C) $48$ (D) $96$ (E) $24$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.