CAT 2019 Shift 1 Paper

Let the work be LCM of (9 and 12$)=36$ units.
Let the amount of work done in one day with their normal efficiencies by $\mathit{A}$ and $\mathit{B}$ be $\mathit{x}$ and $\mathit{y}$ units respectively.
Therefore, $\left(\mathit{x}+\mathit{y}\right)\times 12=36$
Or $\mathit{x}+\mathit{y}=3...\left(1\right)$
Similarly,
$\left(\mathit{x}/2+3\mathit{y}\right)\times 9=36$
Or $\mathit{x}/2+3\mathit{y}=4...\left(2\right)$
Solving (1) and (2) for $\mathit{x},$ we get $\mathit{x}=2$ units
Hence, $\mathit{A}$ alone would take $36/\mathit{x}=36/2=18$ days to complete the work with her normal efficiency.