A can complete a piece of work in 20 days and B can complete the same work in 10 days. With the help of C, working together they completed the work in 5 days. The number of days in which C alone can complete the work is:

The correct answer is 20 (which corresponds to Option 4).

Step 1: Determine the work done by A and B per day.
Let the total work be represented as 1 unit.

Work done by A in 1 day = $\frac{1}{20}$

Work done by B in 1 day = $\frac{1}{10}$

Step 2: Determine the combined work done by A, B, and C per day.
Together with C, they complete the entire work in 5 days.

Work done by (A + B + C) in 1 day = $\frac{1}{5}$

Step 3: Calculate the work done by C alone in 1 day.
The work done by C in 1 day is equal to the combined daily work of all three minus the combined daily work of A and B:

Work done by C in 1 day = $\frac{1}{5}-\left(\frac{1}{20}+\frac{1}{10}\right)$

First, find the sum of A and B's daily work:
$\frac{1}{20}+\frac{1}{10}=\frac{1+2}{20}=\frac{3}{20}$

Now, subtract this from the combined daily work of A, B, and C:
$\text{Work done by C in 1 day}=\frac{1}{5}-\frac{3}{20}=\frac{4-3}{20}=\frac{1}{20}$

Step 4: Find the total days required by C alone.
Since C completes $\frac{1}{20}$ of the work in 1 day, the total number of days C takes to complete the work alone is:

$\text{Total days for C}=\frac{1}{1/20}=20\text{days}$

Therefore, C alone can complete the work in 20 days.