A hostel had rations for 60 days for 500 students. After 12 days, 300 more students join the hostel. How long will the remaining rations last?

To solve this problem, we can calculate the initial amount of rations available for one student per day and then determine how long the remaining rations will last with the increased number of students.

Initially, the hostel had rations for 60 days for 500 students. This means the total rations available were:

Total rations = 60 days * 500 students

Let's calculate the initial ration consumption rate per student per day:

Initial ration consumption rate = Total rations / (60 days * 500 students)

After 12 days, 300 more students join the hostel, so the total number of students becomes 500 + 300 = 800 students.

To calculate how long the remaining rations will last, we can divide the total rations by the new consumption rate for 800 students:

Remaining rations = Total rations / (Consumption rate * Number of students)

Remaining days = Remaining rations / Consumption rate

Let's calculate the remaining days:

Remaining days = (60 days * 500 students) / (Consumption rate * 800 students)

Now, let's calculate the consumption rate:

Consumption rate = Total rations / (60 days * 500 students)

After simplification, we get:

Remaining days = (60 days * 500 students) / ((Total rations / (60 days * 500 students)) * 800 students)

We can cancel out the common terms:

Remaining days = (60 days * 500 students)^2 / (Total rations * 800 students)

Substituting the values:

Remaining days = (60 * 500)^2 / (Total rations * 800)

Since the value of Total rations is not given, we cannot provide an exact number of days. However, if you provide the value of Total rations, I can help you calculate the remaining days.