A School Hostel Has Enough Food For 500 Children For 18 Days. How Long Will The Food Last If 100 More

A School Hostel Has Enough Food For 500 Children For 18 Days. How Long Will The Food Last If 100 More children join the hostel? This question is a classic example of a problem involving proportionality and basic arithmetic calculations. Understanding how to approach such problems is essential for students, teachers, and anyone interested in resource management. In this article, we will explore the problem thoroughly, break down the calculations step-by-step, discuss related concepts, and provide tips for solving similar problems efficiently.

Understanding the Problem

Before diving into calculations, it’s vital to comprehend the scenario fully.

Initial Conditions

• The hostel has enough food to feed 500 children for 18 days.
• The total amount of food is therefore sufficient for these 500 children over this period.

Change in Conditions

• An additional 100 children join the hostel, making the total number of children 600.
• The question is: How long will the existing food last with 600 children?

This problem involves understanding the relationship between the number of children and the duration the food can sustain them.

Key Concepts and Formulas

To solve this problem, we need to understand and apply some fundamental concepts:

1. Total Food Quantity

• The total amount of food can be thought of as a fixed quantity, say, F.
• Since 500 children can be fed for 18 days, we can express F in terms of daily consumption.

2. Daily Consumption

• The total daily consumption for 500 children is proportional to the total food divided by days:

Total daily consumption = F / 18

• For 500 children, the daily consumption is:

Daily consumption per child = (F / 18) / 500

3. Total Food for New Scenario

• When 600 children are fed, the total daily consumption increases proportionally:

Total daily consumption for 600 children = 600 × (F / 18) / 500

• Simplify:

Total daily consumption = (600 / 500) × (F / 18) = (6 / 5) × (F / 18)

4. Duration the Food Will Last

• To find out how many days the same amount of food F will last for 600 children, we use:

Number of days = F / (Daily consumption for 600 children)

• Substituting the value:

Number of days = F / [(6 / 5) × (F / 18)] = 1 / [(6 / 5) × (1 / 18)]

• Simplify the denominator:

(6 / 5) × (1 / 18) = 6 / (5 × 18) = 6 / 90 = 1 / 15

• Therefore:

Number of days = 1 / (1 / 15) = 15 days

This means, with 600 children, the existing food will last for 15 days.

Step-by-Step Calculation Summary

Let's summarize the calculation process:

• Determine total food based on initial conditions: 500 children for 18 days.
• Calculate total daily consumption: total food divided by 18 days.
• Find total daily consumption with 600 children: multiply the per-child consumption by 600.
• Divide the total food by the new daily consumption to find the new duration.

Result: The food will last for 15 days if 100 more children join the hostel.

Additional Related Problems

Understanding this problem opens the door to solving similar resource management questions. Here are some related problems and their approaches:

1. If the number of children increases or decreases, how does the duration change?

• Approach: Use proportionality. If the number of children increases, the duration decreases proportionally, and vice versa.

2. How much food is initially available?

• Approach: Multiply the number of children by the days they can be fed and the per-child daily consumption.

3. What if the food is used at a different rate?

• Approach: Adjust the calculations based on the new consumption rate, following similar proportionality principles.

Practical Applications and Tips

Understanding resource allocation problems is vital in many real-world scenarios, including:

• Managing supplies in disaster relief operations.


• Planning menus and inventory for institutions.


• Budgeting resources for events or large gatherings.

Tips for solving such problems efficiently:

• Always identify the total resource quantity first.
• Express per-unit consumption to facilitate scaling calculations.
• Use proportionality when the number of consumers or duration changes.
• Double-check your units and conversions to avoid mistakes.
• Break down complex problems into smaller, manageable parts, and solve step-by-step.

Conclusion

The question of how long the food will last when 100 more children join the hostel is straightforward once you understand the proportional relationships involved. By analyzing the initial conditions and applying basic arithmetic, we find that the same amount of food, originally sufficient for 500 children for 18 days, will now last for 15 days with 600 children. Such problems reinforce the importance of understanding ratios, proportions, and resource management strategies—skills that are applicable far beyond this specific scenario.

Whether you're a student preparing for exams or a professional involved in logistics and planning, mastering these fundamental concepts can greatly enhance your ability to make informed decisions about resource allocation and sustainability.