Forty five people dig a pond in 18 days. If the pond must be dug in 15 days, how many people are required?

Introduction / Context:
For uniform work rates, the number of worker days (people * days) needed is constant for the same job. If the deadline shortens, more workers are needed proportionally.

Given Data / Assumptions:

• Original team: 45 people.
• Original duration: 18 days.
• New duration: 15 days.
• Equal productivity and identical job.

Concept / Approach:
Total person days for the job are fixed. Compute the total person days from the original plan and divide by the new number of days to get the required team size.

Step-by-Step Solution:

Verification / Alternative check:
Check proportionality: time drops from 18 to 15 (factor 5/6), so workers must rise by factor 6/5: 45 * (6/5) = 54, which matches the computed value.

Why Other Options Are Wrong:
50, 60, 72, 48 do not meet the exact person day requirement 810 and would either leave work incomplete or waste capacity.

Common Pitfalls:
Using an additive rather than multiplicative adjustment; rounding mid calculation; forgetting that person days must remain constant for the same job.

Final Answer:
54