A total of 35 persons are engaged to complete a certain piece of work in 60 days. After 32 days it is found that only two-fifths of the work has been completed. How many persons in total must be working so that the remaining work is finished within the originally planned 60 days?

Introduction / Context:
This question is about workforce adjustment when the actual progress of a project is slower than planned. The work was originally scheduled based on 35 persons working for 60 days, but after 32 days, only two-fifths of the job is complete. We must determine the total number of persons that should now be employed so that the remaining work is finished within the original deadline. This is a typical manpower and time trade-off question in aptitude tests.

Given Data / Assumptions:

• Initial workforce: 35 persons.
• Planned total duration: 60 days.
• Actual progress after 32 days: 2/5 of the work completed.
• Remaining duration: 60 − 32 = 28 days.
• All persons are assumed to work at the same constant rate.
• We are asked for the total number of persons required for the remaining period.

Concept / Approach:
We use the idea of "man-days" as the unit of total effort required for the job. First we compute the amount of work (in man-days) already done and relate it to the fraction of work completed to infer the total work in man-days. Then we find how many man-days are still needed for the remaining fraction. Finally, dividing the required man-days by the remaining days gives the workforce needed. This total includes the original persons plus any additional persons to be engaged.

Step-by-Step Solution:
Step 1: Let total work = 1 unit. Step 2: In 32 days, 35 persons have completed 2/5 of the work. Step 3: Man-days consumed so far = 35 × 32 = 1120 man-days, which correspond to 2/5 of the work. Step 4: Total man-days required for the whole work = 1120 × (5/2) = 2800 man-days. Step 5: Remaining fraction of work = 1 − 2/5 = 3/5. Step 6: Man-days required for remaining work = 2800 × 3/5 = 1680 man-days. Step 7: Remaining time available = 60 − 32 = 28 days. Step 8: Required workforce = 1680 man-days / 28 days = 60 persons.

Verification / Alternative check:
If 60 persons now work for the remaining 28 days, the additional man-days contributed are 60 × 28 = 1680 man-days. Adding the original 1120 man-days gives a total of 2800 man-days, which is exactly the total effort we calculated earlier for completing the job. Also, 2800 man-days divided by 60 planned days is about 46.67 persons on average, which is consistent with needing more than the original 35 persons because the work is behind schedule.

Why Other Options Are Wrong:
45, 50, and 55 persons would supply fewer than 1680 man-days in 28 days, so the remaining work would not be finished in time. For example, 50 persons would give only 50 × 28 = 1400 man-days, short of the 1680 required. 40 persons would be even less. Only 60 persons provide exactly the required 1680 man-days in the remaining 28 days.

Common Pitfalls:
Some students mistakenly compute how many extra persons to add instead of the total, which would be 25 additional persons beyond the original 35. Others forget to translate the fraction of work completed into man-days and directly scale persons in proportion to days, which can be misleading. Always think in terms of total man-days for the whole job, then work backward to the required workforce.

Final Answer:
The total number of persons required to finish the work on time is 60.