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.$\Rightarrow \; \frac{2}{s} = \; \frac{1}{a} + \; \frac{1}{k} --(1)$Also, given that Kamal takes twice as much time as Amal to do the same amount of job$\Rightarrow a = 2k$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 $W$ is the total work $\Rightarrow 4a + 9s + 16k = W$.from (1) $\; \frac{2}{s} = \; \frac{1}{a} + \; \frac{2}{a} \Rightarrow a = \; \frac{3}{2} s$ and $k = \; \frac{3}{4} s$$\Rightarrow 4 \left( \; \frac{3s}{2} \right) + 9s + 16 \left( \; \frac{3s}{4} \right) = W$ $\Rightarrow 6s + 9s + 12s = W$$\Rightarrow 27s = W \Rightarrow s = \; \frac{W}{27}$⇒ Sunil will take 27 days to finish the work when working alone.