A garrison of 1,204 men has provisions for 24 days. How long, in days, will…
2026
A garrison of 1,204 men has provisions for 24 days. How long, in days, will the provisions last if the garrison is increased to 2,064 men?
Answer: C. 14 — ConceptWhen the total quantity of provisions is fixed and each person consumes at the same constant rate, the number of people and the number of days are…
- A.
13
- B.
16
- C.
14
- D.
15
Attempted by 99 students.
Show answer & explanation
Correct answer: C
Concept
When the total quantity of provisions is fixed and each person consumes at the same constant rate, the number of people and the number of days are inversely proportional. The invariant quantity is person-days: people × days = constant.
Application
The original stock equals 1,204 × 24 = 28,896 person-days.
Let d be the duration for 2,064 men. Conservation of person-days gives 2,064d = 28,896.
Therefore, d = 28,896 ÷ 2,064 = 14 days.
Cross-check
The new consumption is 2,064 × 14 = 28,896 person-days, exactly equal to the original stock. Therefore, the provisions will last 14 days.