Question 15.

Let us assume the efficiencies of Amal, Sunil, and Kamal are a, s, and k, respectively.

Given that they are in H.P.

=> $\frac{2}{s} = \frac{1}{a} + \frac{1}{k}$ ---(1)

Also, given that Kamal takes twice as much time as Amal to do the same amount of job

=> 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 => 4a + 9s + 16k = W.

from (1) $\frac{2}{s} = \frac{1}{a} + \frac{2}{a}$ => $a = \frac{3}{2}s$ and $k = \frac{3}{4}s$

=> $4\left(\frac{3s}{2}\right) + 9s + 16\left(\frac{3s}{4}\right) = W$

=> 6s + 9s + 12s = W

=> 27s = W => $s = \frac{W}{27}$

=> Sunil will take 27 days to finish the work when working alone.