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Question

Difficulty: MediumRatio, Proportion, and Rate

A boarding school store has sufficient provisions to feed 120120 students for 2525 days. After 55 days of regular consumption, 3030 additional students join the school. Assuming the daily consumption rate per student remains unchanged, for how many more days will the remaining provisions last?

  1. 16 days16\text{ days}Answer
  2. B
    20 days20\text{ days}
  3. C
    25 days25\text{ days}
  4. D
    24 days24\text{ days}

Answer

The remaining provisions will last for 16 days16\text{ days}.
After 5 days, the remaining food is sufficient to feed 120 students for 20 more days, giving a total of 120×20=2,400120 \times 20 = 2,400 student-days of provisions. When 30 new students join, the group increases to 150 students. Dividing 2,400 student-days by 150 students gives 16 days.

Step-by-Step Solution

1
Calculate the remaining days of food for the original number of students
Remaining days=25−5=20 days\text{Remaining days} = 25 - 5 = 20\text{ days}
Food has already been consumed for 5 days out of the original 25 days.
2
Determine the total remaining food capacity in student-days
Remaining supply=120 students×20 days=2,400 student-days\text{Remaining supply} = 120 \text{ students} \times 20 \text{ days} = 2,400 \text{ student-days}
One student-day represents the amount of food consumed by one student in one day.
3
Calculate the new total number of students
Total students=120+30=150 students\text{Total students} = 120 + 30 = 150 \text{ students}
30 additional students joined the original 120 students.
4
Find the number of days the remaining food will last the new total number of students
Days=2,400 student-days150 students=16 days\text{Days} = \frac{2,400 \text{ student-days}}{150 \text{ students}} = 16 \text{ days}
Since consumption rate is inversely proportional to the number of consumers, divide total student-days by the total student count.

Key Concept

Inverse Proportion and Consumption Rate
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Topics

Ratio, Proportion, and Rate

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