Working together A, B and C can complete a piece of work in $24$ days. After working together for $4$ days, C left the work. A and B completed the remaining work in $30$ days. The number of days taken by C alone to complete the same work is:

Let the total work be such that the combined efficiency of $(A+B+C)=1\text{ unit/day}$. $$\text{Total work}=\text{Efficiency}\times \text{Time}=1\times 24=24\text{ units}$$
They work together for $4$ days:
$$\text{Work completed in 4 days}=1\times 4=4\text{ units}$$
$$\text{Remaining work}=24-4=20\text{ units}$$
This remaining $20\text{ units}$ of work is completed by A and B in $30$ days:
$$\text{Efficiency of }(A+B)=\frac{\text{Remaining Work}}{\text{Time}}=\frac{20}{30}=\frac{2}{3}\text{ units/day}$$
Now, we find the individual efficiency of C:
$$\text{Efficiency of C}=\text{Efficiency of }(A+B+C)-\text{Efficiency of }(A+B)$$
$$\text{Efficiency of C}=1-\frac{2}{3}=\frac{1}{3}\text{ units/day}$$
The time taken by C alone to complete the total work is:
$$\text{Time}=\frac{\text{Total Work}}{\text{Efficiency of C}}=\frac{24}{\frac{1}{3}}=24\times 3=72\text{ days}$$