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Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The numbers $a$ , $b$ , $c$ and $d$ are distinct positive integers chosen from $1$ to $10$ inclusive. What is the least possible value $\dfrac{a}{b} + \dfrac{c}{d}$ could have?

(A) $\dfrac{2}{10}$ (B) $\dfrac{3}{19}$ (C) $\dfrac{14}{45}$ (D) $\dfrac{29}{90}$ (E) $\dfrac{25}{72}$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.