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

Solution(By Examveda Team)

Let's denote the number of students originally in the dormitory as S and the number of new students admitted as N.
Originally, there was enough food for 300 students for 15 days. This can be expressed as:
     \(300 \, \text{students} \times 15 \, \text{days} = 4500 \, \text{student-days}\)

After admitting new students, the food only lasted for 10 days:
     \((S + N) \times 10 \, \text{days} = 4500 \, \text{student-days}\)

Now we can set up an equation based on this information:
     \(300 \times 15 = (S + N) \times 10\)

Solving for S + N (total number of students after admission of new students):
     \(4500 = (S + N) \times 10\)

Divide both sides by 10:
     \(450 = S + N\)

Now, we also know that the food was originally enough for S students for 15 days, and after new students were admitted, it only lasted for 10 days. So, we can set up another equation:
     \(S \times 15 = (S + N) \times 10\)

Solving for S:
     \(15S = 10S + 10N\)

Subtract \(10S\) from both sides:
     \(5S = 10N\)

Divide both sides by 5:
     \(S = 2N\)

Now, substitute \(S = 2N\) into the first equation:
     \(450 = 2N + N\)

Combine like terms:
     \(450 = 3N\)

Divide both sides by 3:
     \(N = 150\)

So, 150 new students were admitted to the dormitory.