Manav and Manu can complete a piece of work in $16$ days and $24$ days, respectively. They worked together for $8$ days, after which Manav leaves. In how many days can Manu finish the remaining work?

Let's calculate the total work and efficiencies using the LCM method:
* Time taken by Manav = $16\text{ days}$
* Time taken by Manu = $24\text{ days}$

Let the Total Work be the LCM of $16$ and $24$, which is $48\text{ units}$.

Now, find the daily efficiency (work done per day):

* Efficiency of Manav = $\frac{48}{16}=3\text{ units/day}$
* Efficiency of Manu = $\frac{48}{24}=2\text{ units/day}$
* Combined efficiency of both = $3+2=5\text{ units/day}$

They worked together for $8$ days:

$$\text{Work done in 8 days}=8\times 5=40\text{ units}$$

Calculate the remaining work:

$$\text{Remaining Work}=48-40=8\text{ units}$$

Now, Manav leaves, and Manu has to complete the remaining work alone:

$$\text{Time taken by Manu}=\frac{\text{Remaining Work}}{\text{Efficiency of Manu}}=\frac{8}{2}=4\text{ days}$$

Thus, Manu will finish the remaining work in $4$ days.