A is three times more efficient than B and together they finish a piece of work in $30$ days. In how many days can A alone finish the same work?

Let's focus carefully on the phrase "three times more efficient than B".
In standard competitive exams like SSC, "three times more efficient" or "three times as efficient" translates directly to the mathematical efficiency ratio:
$$\text{Efficiency of A}:\text{Efficiency of B}=3:1$$

Let:
* Efficiency of B = $1\text{ unit/day}$
* Efficiency of A = $3\text{ units/day}$
* Combined efficiency of A and B = $3+1=4\text{ units/day}$

They can complete the work together in $30$ days:
$$\text{Total Work}=\text{Combined Efficiency}\times \text{Time}=4\times 30=120\text{ units}$$

The time taken by A alone to finish the same work is:
$$\text{Time taken by A}=\frac{\text{Total Work}}{\text{Efficiency of A}}=\frac{120}{3}=40\text{ days}$$