Twenty eight women can complete a certain piece of work in 36 days. If 4 women leave after working for 18 days, how many additional days will be needed to finish the remaining work?

Introduction / Context:
This time and work problem involves a change in the size of the workforce halfway through a job. After a certain period some workers leave, and we are asked to compute the extra time needed to complete the remaining work with fewer workers. It tests understanding of total work in man days or woman days and the effect of changing the number of workers.

Given Data / Assumptions:

• 28 women can complete the work in 36 days.
• All 28 women initially work for 18 days.
• After 18 days, 4 women leave, so 24 women continue.
• The work rate of each woman is constant throughout.
• We must find how many days the remaining 24 women need to complete the remaining work.

Concept / Approach:
We treat the total work in terms of woman days. If W is the total work, then W = number of women multiplied by number of days, assuming one unit of work per woman per day. After computing W, we calculate how much work is done in the first phase with 28 women for 18 days, subtract that from the total work and then divide the remainder by the daily capacity of 24 women to get the additional days required.

Step-by-Step Solution:
Step 1: Let work done per woman per day be 1 unit. Then total work W = 28 women * 36 days = 1008 woman days.Step 2: Work completed in the first 18 days with 28 women = 28 * 18 = 504 woman days.Step 3: Remaining work = total work - work already done = 1008 - 504 = 504 woman days.Step 4: After 4 women leave, number of women remaining = 28 - 4 = 24.Step 5: Daily work capacity of the remaining group = 24 woman days per day.Step 6: Days required to finish remaining work = remaining work / daily capacity = 504 / 24.Step 7: Compute 504 / 24. Divide numerator and denominator by 8: 504 / 24 = 63 / 3 = 21 days.

Verification / Alternative check:
We can check that the total calendar days are 18 (before women leave) plus 21 (after some leave) = 39 days. If 24 women had worked alone from the beginning at the same rate, time would have been total work divided by 24, that is 1008 / 24 = 42 days, which is longer. This makes sense because initially there were more workers. The internal calculation remains consistent, confirming that 21 days of additional work is correct.

Why Other Options Are Wrong:

• 24 days: This would mean total woman days after reduction is 24 * 24 = 576, which exceeds the remaining work of 504.
• 27 days: This would give 24 * 27 = 648 woman days, also more than needed.
• 25 days: This implies 600 woman days, still more than 504, making it inconsistent with the original total work.

Common Pitfalls:
Some students miscalculate the total work or forget that the number of workers changes midway. Another frequent mistake is to average the number of workers over the entire duration instead of correctly splitting the work into phases. Always compute total work first, then account for each phase of the work with the correct number of workers.

Final Answer:
The remaining work will be completed in 21 additional days.