A piece of work could originally be finished in 11 days by a certain number of men. However, 4 more men joined from the beginning, and as a result the work was completed 4 days earlier. How many men were originally employed to do the work?

Introduction / Context:
This question is about how adding more workers affects the completion time of a job. We are told that there was an original plan to finish a job in 11 days, but after increasing the workforce from the start by 4 men, the job finished 4 days earlier. We must determine the original number of men. This is a standard Time and Work scenario that uses the idea that total work is proportional to (number of men) * (time).

Given Data / Assumptions:

• Originally, some men working together could finish a job in 11 days.
• From the very beginning, 4 extra men joined the original group.
• With this increased workforce, the job finished 4 days earlier, i.e., in 7 days.
• All men have equal and constant efficiency.
• Total work is considered as 1 unit.

Concept / Approach:
Let the original number of men be m and each man's daily work rate be r units per day. Then the total work is m * r * 11. After 4 additional men join from the start, the new workforce is (m + 4) men, and they finish the same work in 7 days, so total work is also (m + 4) * r * 7. Since total work is unchanged, these two expressions must be equal. From this equation, we can solve for m. The rate r cancels out, leaving a simple algebraic equation in m only.

Step-by-Step Solution:
Let m be the original number of men. Let each man's daily work rate be r units. Total work W = m * r * 11 (original plan). With 4 more men from the start, number of men = m + 4. New time taken = 11 - 4 = 7 days. Total work W is also equal to (m + 4) * r * 7. Since both expressions equal the same work: m * r * 11 = (m + 4) * r * 7. Cancel r from both sides: 11m = 7(m + 4). 11m = 7m + 28. 11m - 7m = 28 ⇒ 4m = 28. m = 28 / 4 = 7. Thus, originally there were 7 men employed.

Verification / Alternative check:
Originally, 7 men would finish the work in 11 days, so total work = 7 * 11 = 77 man-days. With 4 extra men, total men = 11. Time taken with 11 men = total work / men = 77 / 11 = 7 days, which matches the statement that the work was finished 4 days earlier (11 - 7 = 4 days). Hence our value m = 7 is consistent with all the data given.

Why Other Options Are Wrong:
If m were 8, total work would be 8 * 11 = 88 man-days, and with 12 men the time would be 88 / 12 ≈ 7.33 days, not an exact 4-day reduction. Similarly, with m = 9 or 10, the resulting times do not provide exactly 4 days of savings and do not satisfy the equality between the two work expressions. Only m = 7 gives a precise match to the problem conditions.

Common Pitfalls:
A typical mistake is to misinterpret the phrase "finished 4 days earlier" as meaning that the extra men joined sometime in the middle of the project instead of from the beginning. In that case, more unknown variables arise, and the problem becomes ambiguous. However, the usual interpretation in such aptitude questions is that the extra workers are counted from day one. Another error is forgetting to cancel the common rate r and thus overcomplicating the algebra.

Final Answer:
The number of men originally employed to do the work was 7 men.