A and B can complete a task in 30 days when working together. After A and B have been working together for 11 days, B is called away and A, all by himself completes the task in the next 28 days. Had A been working alone, the number of days taken by him to complete the task would have been.
Solution
A and B can complete a task in 30 days.
Work done by A and B in 1 day $= \dfrac{1}{30}$
Work done by A and B in 11 days $= \dfrac{11}{30}$
Remaining work $\Rightarrow 1 - \dfrac{11}{30} = \dfrac{19}{30}$
Remaining work $\left( \dfrac{19}{30}\right)$ is completed by A in 28 days.
so, A will alone completes the work in $= \dfrac{28 \times 30}{19}$
$= 44\dfrac{4}{19}$ days