MAT Exam 2021 Paper

Concept:Work is treated as $1$ complete unit. Use the combined one-day work to find remaining work, then use $A$'s time to find his alone time.Explanation:$A$ and $B$ together finish the task in $30$ days.So, their combined one-day work is $\frac{1}{30}$.Work done by both in $11$ days is:$$11 \times \frac{1}{30} = \frac{11}{30}$$Remaining work after $11$ days is:$$1 - \frac{11}{30} = \frac{19}{30}$$$A$ completes this remaining $\frac{19}{30}$ of the work in $28$ days.Hence, $A$'s one-day work is:$$\frac{\frac{19}{30}}{28} = \frac{19}{840}$$Time taken by $A$ alone to complete the whole task is:$$\frac{1}{\frac{19}{840}} = \frac{840}{19} = 44\frac{4}{19}$$Thus, $A$ alone would take $44\frac{4}{19}$ days.Answer:Option C: $44\frac{4}{19}$ days.