X people were given a contract for doing a piece of work in 18 days. 2 people did not turn up to work due to sickness, and the rest of the people completed the work in 27 days. What is the value of X?

The correct option is 6.

Let us understand the problem step-by-step using the concept of man-days (the total amount of work done). The total work is equal to the product of the number of people and the number of days they work.

Initially, $X$ people were contracted to complete the work in 18 days.
Therefore, the total work can be represented as:
Total Work = $X\times 18$ man-days

However, 2 people did not turn up. This means the actual number of people who worked is:
$(X-2)$ people

These remaining people completed the same piece of work in 27 days.
So, the total work can also be represented as:
Total Work = $(X-2)\times 27$ man-days

Since the total work remains constant in both cases, we can equate the two expressions:
$18X=27(X-2)$

Now, let us solve the equation for $X$:
Divide both sides by 9 to simplify the numbers:
$2X=3(X-2)$

Expand the right side:
$2X=3X-6$

Rearrange the equation to isolate $X$:
$3X-2X=6$
$X=6$

Thus, the value of $X$ is 6, indicating that 6 people were initially contracted for the work.