X is able to complete a task in 12 days, while Y takes 18 days to finish the same task. If they collaborate and work together for 3 days, what fraction of the work will still remain?

The correct option is $\frac{7}{12}$.

Step 1: Determine the work done by X and Y in one day.
Let the total work to be completed be represented as 1 unit.
X can complete the entire task in 12 days, so the fraction of work done by X in 1 day is:

$\frac{1}{12}$

Y can complete the entire task in 18 days, so the fraction of work done by Y in 1 day is:

$\frac{1}{18}$

Step 2: Calculate their combined work in one day.
When X and Y work together, the total fraction of work done in 1 day is the sum of their individual daily work rates:

$\frac{1}{12}+\frac{1}{18}$

To add these fractions, find the least common multiple (LCM) of the denominators 12 and 18, which is 36:

$\frac{3}{36}+\frac{2}{36}=\frac{5}{36}$

So, working together, X and Y complete $\frac{5}{36}$ of the task per day.

Step 3: Calculate the total work completed in 3 days.
In 3 days of working together, the fraction of work completed is:

$3\times \frac{5}{36}=\frac{15}{36}=\frac{5}{12}$

Step 4: Find the fraction of work that remains.
Subtract the completed fraction of work from the total work (1):

$1-\frac{5}{12}=\frac{12-5}{12}=\frac{7}{12}$

Therefore, the fraction of work remaining after 3 days is $\frac{7}{12}$.