Man-days constant for fixed work: A stock of food is sufficient for 240 men for 48 days. For how many days will the same stock last for 160 men, assuming equal daily consumption per man?
Aptitude
Time and Work
Difficulty: Easy
Choose an option
Answer
Correct Answer: 72 days
Explanation
Introduction / Context:Food-stock questions rely on the constancy of total consumption measured in man-days. If the number of men changes, the duration adjusts inversely so that (men * days) remains constant, provided per-man consumption is unchanged.
Given Data / Assumptions:
- Initial: 240 men for 48 days.
- All men consume equal amounts per day; no wastage.
- New team size: 160 men.
Concept / Approach:Total stock S (in man-days) = men * days. New days = S / new_men.
Step-by-Step Solution:S = 240 * 48 = 11520 man-days.For 160 men, days = 11520 / 160 = 72 days.
Verification / Alternative check:Proportionality: Reducing men from 240 to 160 is multiplying by 160/240 = 2/3; days should increase by 3/2: 48 * 1.5 = 72 days.
Why Other Options Are Wrong:
- 54, 60, 64 do not satisfy S = 11520 when multiplied by 160.
Common Pitfalls:
- Adding/subtracting days linearly instead of using the product men * days.
Final Answer:72 days