CAT 2023 Slot 1 Solved Paper

Let us assume the efficiencies of Amal, Sunil, and Kamal are a, s, and k, respectively.
Given that they are in H.P.
$\Rightarrow \frac{2}{\mathit{s}}=\frac{1}{\mathit{a}}+\frac{1}{\mathit{k}}--\left(1\right)$
Also, given that Kamal takes twice as much time as Amal to do the same amount of job
$\Rightarrow \mathrm{a}=2\mathrm{k}$
Given that when Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job.
⇒ If $\mathrm{W}$ is the total work $\Rightarrow 4\mathrm{a}+9\mathrm{}\mathit{s}+16\mathrm{k}=\mathrm{W}$.
from (1) $\frac{2}{\mathit{s}}=\frac{1}{\mathit{a}}+\frac{2}{\mathit{a}}\Rightarrow \mathit{a}=\frac{3}{2}\mathit{s}$ and $\mathit{k}=\frac{3}{4}\mathit{s}$
$\Rightarrow 4\left(\frac{3\mathit{s}}{2}\right)+9\mathit{s}+16\left(\frac{3\mathit{s}}{4}\right)=\mathit{W}$
$\Rightarrow 6\mathit{s}+9\mathit{s}+12\mathit{s}=\mathit{W}$
$\Rightarrow 27\mathit{s}=\mathit{W}\Rightarrow \mathit{s}=\frac{\mathit{W}}{27}$
⇒ Sunil will take 27 days to finish the work when working alone.