Rations are provided to feed 72 soldiers for 54 days. If the same stock is used to feed 90 soldiers but the individual ration is reduced by 10%, how long will the food last?

Introduction: When headcount changes and per-person ration also changes, convert everything to “soldier-equivalent” days. A 10% reduction means each soldier consumes 0.9 of the original daily ration, so 90 soldiers consume the equivalent of 81 “full-ration” soldiers per day. Apply man-day conservation to compute the new duration.

Given Data / Assumptions:

• Original: 72 soldiers for 54 days → stock = 72 * 54 full-ration soldier-days.
• New: 90 soldiers at 90% ration → effective daily consumption = 90 * 0.9 = 81 full-ration soldier-days/day.
• Consumption is uniform; no wastage.

Concept / Approach: Let S be the total stock in full-ration soldier-days. Then duration D satisfies S = 81 * D. Compute S from the original configuration and divide by 81 to find D in days.

Step-by-Step Solution:

Verification / Alternative check: Simplify first: 72/81 = 8/9; thus D = (8/9)*54 = 8*6 = 48 days, confirming without large numbers.

Why Other Options Are Wrong: 72 or 54 days ignore the ration cut effect; 126 and 36 are inconsistent with the effective 81-soldier-per-day consumption.

Common Pitfalls: Treating 90 soldiers at 90% ration as 90 full-ration soldiers (it is effectively 81), or forgetting to convert to full-ration equivalents.

Final Answer: 48 days