B & C can complete a task in $40$ days while A, B & C can complete the task in $20$ days. In how many days can A complete the task alone?

Let the total work be the LCM of $40$ and $20$, which is $40$ units.
* Combined efficiency of B and C $=\frac{40}{40}=1\text{ unit/day}$
* Combined efficiency of A, B, and C $=\frac{40}{20}=2\text{ units/day}$

To find A's individual efficiency:

$$\text{Efficiency of A}=(\text{Efficiency of A + B + C})-(\text{Efficiency of B + C})$$

$$\text{Efficiency of A}=2-1=1\text{ unit/day}$$

Number of days required by A to complete the task alone:

$$\text{Days}=\frac{\text{Total Work}}{\text{Efficiency of A}}=\frac{40}{1}=40\text{ days}$$