$A$ takes $15$ days; $B$ takes $20$ days. They work together for $5$ days. The fraction of work left is:

$A$ takes $15$ days; $B$ takes $20$ days. They work together for $5$ days. The fraction of work left is:
  1. $\dfrac{1}{6}$
  2. $\dfrac{5}{12}$
  3. $\dfrac{7}{12}$
  4. $\dfrac{1}{2}$

Solution

Combined rate $= \dfrac{1}{15} + \dfrac{1}{20} = \dfrac{4 + 3}{60} = \dfrac{7}{60}$. In $5$ days: $\dfrac{35}{60} = \dfrac{7}{12}$. Left $= 1 - \dfrac{7}{12} = \dfrac{5}{12}$.

Asked in: IMO

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