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.

The correct answer is 4.

Step 1: Understand the given work rates.
We are given that Arvind works 4 times as fast as Suresh.
This means Arvind's efficiency or rate of work is 4 times Suresh's rate of work.

Step 2: Find Suresh's rate of work.
Suresh can complete the entire work independently in 20 days.
Therefore, the fraction of work Suresh completes in 1 day is:

$\text{Suresh's 1-day work}=\frac{1}{20}$

Step 3: Find Arvind's rate of work.
Since Arvind works 4 times as fast as Suresh, Arvind's 1-day work is 4 times Suresh's 1-day work:

$\text{Arvind's 1-day work}=4\times \frac{1}{20}=\frac{4}{20}=\frac{1}{5}$

Step 4: Find their combined 1-day work.
When Arvind and Suresh work together, we add their individual 1-day work rates:

$\text{Combined 1-day work}=\frac{1}{20}+\frac{1}{5}$

Taking a common denominator of 20:

$\text{Combined 1-day work}=\frac{1+4}{20}=\frac{5}{20}=\frac{1}{4}$

Step 5: Calculate the total days required together.
Since together they complete $\frac{1}{4}$ of the total work in 1 day, the total number of days taken by Arvind and Suresh together to finish the work is the reciprocal of their combined 1-day work rate:

$\text{Total Days}=4\text{days}$

Thus, Arvind and Suresh working together can complete the work in 4 days.