Arvind works $4$ times as fast as Suresh. If Suresh can complete a work in $20$ days independently, then find the number of days in which Arvind and Suresh can together finish the work.

Let the efficiency of Suresh be $1\text{unit/day}$.
Since Arvind works $4$ times as fast as Suresh, the efficiency of Arvind = $4\text{units/day}$.

Suresh completes the work independently in $20$ days.

$$\text{Total Work}=\text{Efficiency of Suresh}\times \text{Time taken}$$

$$\text{Total Work}=1\times 20=20\text{units}$$

The combined efficiency of Arvind and Suresh together:

$$\text{Combined Efficiency}=4+1=5\text{units/day}$$

The number of days required for both to finish the work together:

$$\text{Time taken together}=\frac{\text{Total Work}}{\text{Combined Efficiency}}=\frac{20}{5}=4\text{days}$$