A hostel has sufficient food for 200 students for 50 days. after 10 days, 50 more students join the hostel. now, the food will continue for how many days?

a hostel has sufficient food for 200 students for 50 days. after 10 days, 50 more students join the hostel. now, the food will continue for how many days?

a hostel has sufficient food for 200 students for 50 days. after 10 days, 50 more students join the hostel. now, the food will continue for how many days?

Answer: Let’s calculate how much food the hostel has initially:

Food for 200 students for 50 days.

Total food = 200 students * 50 days = 10,000 student-days of food.

Now, after 10 days, some of the food has been consumed. So, the remaining food can sustain:

Remaining food = Total food - Food consumed in 10 days
Remaining food = 10,000 student-days - (200 students * 10 days) = 10,000 student-days - 2,000 student-days = 8,000 student-days of food.

Now, 50 more students join the hostel, so the total number of students becomes 200 + 50 = 250 students.

To find out how many more days this remaining food will last for 250 students, we can set up a proportion:

(Remaining food) / (Number of students * Number of days) = (8,000 student-days) / (250 students * X days)

Now, solve for X:

X = (8,000 student-days) / (250 students * X days)

Cross-multiply:

8,000 * X = 250 students * X days

Now, divide both sides by 250 students:

X = (8,000 student-days) / (250 students) = 32 days.

So, the remaining food will continue to sustain 250 students for 32 more days.