Question

The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is

Answer 1

The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression.
\(⇒ \) This implies that the amount of time taken individually by Amal, Sunil and Kamal to finish a job are in A.P.
Kamal requires twice the time Amal does to complete the same amount of work. As the time taken by each person follows an arithmetic progression, this implies that Sunil should take \(1.5\) times longer than Amal to complete the same task.
Thus, the ratio of time taken by Amal, Sunil, and Kamal to complete the same amount of work individually is either \(1:1.5:2 \) or \(2:3:4\).
Given that Amal, Sunil, and Kamal took \(4, 9,\) and \(16\) days respectively to finish the job, we can deduce further relationships:
Sunil completes in \(3\) days what Amal does in \(2\) days.
Therefore, Sunil completes in \(6\) days what Amal does in \(4\) days.
Sunil completes in \(3\) days what Kamal does in \(4\) days.
Therefore, Sunil completes in \(12\) days what Kamal does in \(16\) days.
Hence, to complete the entire job independently, Sunil would require a total of \(6 + 9 + 12 = 27\) days.

So, the answer is \(27\) days.