In 11 days, only 1/6 of the work was done. It is evident that the remaining 5/6 of the work will be finished within 55 days.

To solve this problem, we can use the concept of man-days.

Given:
- The job is to be completed in 55 days.
- 48 men were initially employed.
- In 11 days, only 1/6 of the work was completed.

Let's assume that the total work required for the job is represented by W.

Work done in 11 days:
In 11 days, only 1/6 of the work was completed.
So, the work done in 11 days = (1/6) * W = W/6

Work remaining after 11 days:
Work remaining = Total work - Work done in 11 days = W - W/6 = (5W/6)

Time remaining:
Since the job is to be completed in 55 days and 11 days have already passed, the time remaining is 55 - 11 = 44 days.

Man-days required to complete the remaining work:
Man-days required = (Work remaining) * (Time remaining)
= (5W/6) * 44

Man-days available with 48 men in 44 days:
Man-days available = (Number of men) * (Time remaining)
= 48 * 44

To calculate the number of extra men required, we need to find the difference between the required man-days and the available man-days.

Difference = Man-days required - Man-days available
= (5W/6) * 44 - (48 * 44)
= (5W - 48 * 6) * 44/6

To complete the work in the allotted time, the contractor needs to employ extra men. The number of extra men required can be calculated by dividing the difference by the number of man-days a single man can contribute in a day.

Number of extra men required = Difference / (Man-days contributed by a single man in a day)

Let's assume that each man contributes M man-days in a day.

Number of extra men required = Difference / M

Since we want to find the number of extra men required, we can rearrange the equation as:

M = Difference / (Number of extra men required)

Simplifying, we get:

Number of extra men required = Difference / M = Difference / (Difference / (Number of extra men required))

Simplifying further, we get:

Number of extra men required = Difference * (Number of extra men required) / Difference

The difference cancels out, and we are left with:

Number of extra men required = Number of extra men required

Therefore, any number of extra men would be required to complete the work in the allotted time.