In a student dormitory there was enough food to feed 300 students for 15 days, Became of admission of some new students the food only lasted for 10 days . How many new students are admitted to the dormitory?

Let's denote the initial number of students in the dormitory as "N," and the rate at which food is consumed by each student per day as "R" (measured in student-days per day). We're given that initially, there was enough food to feed 300 students for 15 days, so:

Initial food supply = N * R * 15

Now, due to the admission of some new students, the food only lasted for 10 days, so:

Remaining food supply = (N + X) * R * 10, where "X" represents the number of new students admitted.

Since the amount of food is the same in both cases, we can set the two expressions equal to each other:

N * R * 15 = (N + X) * R * 10

Now, we can cancel out the common factor of "R" on both sides of the equation:

N * 15 = (N + X) * 10

Now, we can solve for "X," the number of new students admitted:

15N = 10(N + X)

15N = 10N + 10X

Subtract 10N from both sides:

5N = 10X

Divide both sides by 5 to solve for "X":

X = (5N) / 10

X = (1/2) * N

Now, we're given that X should be an integer because we can't admit a fraction of a student. Therefore, (1/2) * N must be a whole number.

To find out how many new students were admitted, we need to find a value of "N" where (1/2) * N is a whole number. Since we're looking for the number of new students, we want to find a value of "N" such that (1/2) * N is an integer.

If we let "N" be a multiple of 2, then (1/2) * N will be a whole number. Let's try "N = 300" because it's given that initially, there was enough food for 300 students:

X = (1/2) * 300 X = 150

So, if "N" was initially 300 students, then 150 new students were admitted to the dormitory.