Question 22.

Let Jack take $t$ days to complete the work, then John will take $2t$ days to complete the work. So work done by Jack in one day is $\frac{1}{t}$ and John is $\frac{1}{2t}$.

Now let Jim take $m$ days to complete the work. According to question,

$\frac{1}{t} + \frac{1}{m} = \frac{3}{2t}$ or $\frac{1}{m} = \frac{1}{2t}$

or

$m = 2t$ Hence Jim takes $2t$ time to complete the work.

Now let the three of them complete the work in $p$ days. Hence John takes $p+3$ days to complete the work.

$\frac{1}{2t}(m+3) = \frac{4}{2t}m$

or

$\frac{1}{2t}(m+3) = \frac{4}{2t}m$

or $m=1$. Hence Jim will take $(1+3)=4$ days to complete the work. Similarly John will also take 4 days to complete the work.