Ramu can build a wall alone in $15\text{ days}$, while Ravan can build it alone in $10\text{ days}$. Ramu worked for $5\text{ days}$. Then Ravan joined Ramu for the next $3\text{ days}$. How many more days could Ramu take to build the remaining wall?

Let the total work be the LCM of $15$ and $10$, which is $30\text{ units}$.Efficiency of Ramu:
$${\text{Efficiency}}_{\text{Ramu}}=\frac{30}{15}=2\text{ units/day}$$
Efficiency of Ravan:
$${\text{Efficiency}}_{\text{Ravan}}=\frac{30}{10}=3\text{ units/day}$$
Work done by Ramu alone in the first $5\text{ days}$:
$${\text{Work}}_1=5\times 2=10\text{ units}$$
Work done by Ramu and Ravan together in the next $3\text{ days}$:
$$\text{Combined Efficiency}=2+3=5\text{ units/day}$$
$${\text{Work}}_2=3\times 5=15\text{ units}$$
Total work completed so far:
$$\text{Total Completed}=10+15=25\text{ units}$$
Remaining work:
$$\text{Remaining Work}=30-25=5\text{ units}$$
Time taken by Ramu alone to finish the remaining work:
$$\text{Time}=\frac{\text{Remaining Work}}{{\text{Efficiency}}_{\text{Ramu}}}=\frac{5}{2}=2.5\text{ days}$$