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?

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