A can do a piece of work in 9 days. B can do it in 9 days. With the assistance of C, they completed the work in 3 days. C alone can do it in ______________days.

Correct option is C

Given:
A can complete the work in 9 days
B can complete the work in 9 days
Together with C, they complete the work in 3 days
Concept Used:
Work done = 1 / Time taken
Solution:
If A can complete the work in 9 days, then A's rate of work is $$\frac 19$$​.
Similarly, B’s rate of work is also$$\frac 19$$​
Let C’s rate of work be $$\frac 1x$$​​
When A, B, and C work together, they complete the work in 3 days, so their combined rate is $$\frac 13$$​
​$$\begin{align*}\frac{1}{9} + \frac{1}{9} + \frac{1}{x} &= \frac{1}{3} \\\frac{2}{9} + \frac{1}{x} &= \frac{1}{3} \\\frac{1}{x} &= \frac{1}{9} \\x &= 9\end{align*}$$​​
So, C completed the whole work in 9 days
Alternate Solution:

Efficiency of C = 3 - 1- 1 = 1unit per day
Total time taken by C to complete the work = $$\frac{9}{1} = 9$$ days​