In a hostel of 50 girls, there food provisions are for 40 days. If 30 more girls join the hostel, how long will these provisions last?


This is a classic problem involving proportionality. The food provisions are enough for 50 girls for 40 days, and now 30 more girls are joining the hostel, making a total of \(50 + 30 = 80\) girls. 

The key concept here is that the total amount of food available remains the same, but the number of girls consuming it increases. So, as the number of girls increases, the number of days the provisions last will decrease proportionally.

The relationship can be set up as follows:
\[
\text{Number of girls} \times \text{Number of days} = \text{Constant amount of food}
\]

For the original situation:
\[
50 \times 40 = 2000 \text{ girl-days of food}
\]

Now, with 80 girls, let the number of days the provisions will last be \(x\):
\[
80 \times x = 2000
\]

Solving for \(x\):
\[
x = \frac{2000}{80} = 25 \text{ days}
\]

Thus, if 30 more girls join, the provisions will last for **25 days**.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand on this concept:
1. What happens if only 20 more girls join the hostel instead of 30?
2. How would the situation change if there were provisions for only 30 days for 50 girls?
3. If the number of girls had doubled, how long would the provisions last?
4. What if the provisions were increased by 25%? How long would they last for 80 girls?
5. Can you calculate how much food is consumed by each girl per day?

**Tip:** When solving proportion problems, always identify what remains constant and then set up a proportionality equation accordingly.

In a hostel of 50 girls, there food provisions are for 40 days. If 30 more girls join the hostel, how long will these provisions last?

Solve a proportionality problem where food provisions for 50 girls for 40 days need to be adjusted after 30 more girls join the hostel. Learn the step-by-step solution to find out how long the food will last for 80 girls. Suitable for students in Grades 6-8.

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