Work-rate scaling (pumps and time): Three pumps working 8 hours/day empty a tank in 2 days. How many hours/day should four pumps work to empty the same tank in 1 day (same efficiency)?

Introduction / Context:
Work completed is proportional to (number of pumps) * (hours per day) * (days), assuming constant efficiency. We match total pump-hours between scenarios to keep the completed work equal and solve for the unknown daily hours.

Given Data / Assumptions:

• Scenario 1: 3 pumps * 8 h/day * 2 days
• Scenario 2: 4 pumps * H h/day * 1 day
• Same tank, same efficiency

Concept / Approach:
Equate total pump-hours in both scenarios. This linear direct-proportion model is the foundation of most pump/work/time aptitude questions and is identical to man-hour logic in work-rate problems.

Step-by-Step Solution:

Verification / Alternative check:
With 4 pumps for 12 hours, total pump-hours = 48, matching the first scenario. Therefore, the same amount of work (the tank) is completed in 1 day.

Why Other Options Are Wrong:

• 10, 8, 9, 15: Do not yield 48 pump-hours when multiplied by 4, so the total work would be underdone or overdone relative to the tank’s requirement.

Common Pitfalls:
Forgetting to multiply by the number of days, or trying to average hours without accounting for the change in pump count. Always use total pump-hours equivalence.

Final Answer:
12