A and B can complete a work in $16$ days and $12$ days respectively. Both work for $4$ days and then A leaves. Find how much time will B take to complete the remaining work?

Let the total work be the LCM of $16$ and $12$, which is $48$ units.Efficiency of A = $\frac{48}{16}=3\text{ units/day}$ Efficiency of B = $\frac{48}{12}=4\text{ units/day}$ Combined efficiency of A and B = $3+4=7\text{ units/day}$ They work together for $4$ days:
$$\text{Work completed in 4 days}=7\times 4=28\text{ units}$$
$$\text{Remaining work}=48-28=20\text{ units}$$
Now A leaves, and B completes the remaining work:
$$\text{Time taken by B}=\frac{\text{Remaining work}}{\text{Efficiency of B}}=\frac{20}{4}=5\text{ days}$$