Sarthak and Mohan are working on alternate days in a workshop. Sarthak can complete the work in $20$ days while Mohan can finish in $25$ days. Sarthak works on the 1st day, Mohan on the 2nd day, and so on. How much time (in days) will they take on alternate basis?

Let the total work be the LCM of $20$ and $25=100$ units.Efficiency of Sarthak ($E_S$) = $\frac{100}{20}=5$ units/dayEfficiency of Mohan ($E_M$) = $\frac{100}{25}=4$ units/dayIn a 2-day cycle (Day 1: Sarthak, Day 2: Mohan):Work done in $2$ days = $5+4=9$ units.Number of complete cycles to get close to $100$:
$$11\times 9=99\text{ units}$$
This takes $11\times 2=22$ days.Remaining work after $22$ days = $100-99=1$ unit.On the $23\text{rd}$ day, it is Sarthak's turn.Time taken by Sarthak to complete the remaining $1$ unit = $\frac{1}{5}$ day.Total time taken = $22+\frac{1}{5}=22\frac{1}{5}$ days.