Question:
Eight students of average 13 years leave a class of 30 students of average age 15 years. If seven new students of average 12 years join the class, find the present average age of the students in the class

Answer:
Remember that, at all times: 
Average age of n students = total age of n students / n
Similarly, if the average age is x, for n students, total age = average * number
of students = n*x

Using these, we can solve the problem.

Initially the class has 30 students of average age 15.
Total age of 30 students = 30*15 = 450

8 students of average age 13 leave the class.
Total age of students who left = 8*13 = 104

Number of students left = 30 - 8 = 22
Total of the students left = 450 - 104 = 346

Now, 7 students of average age 12 are added.
Total age of new students = 7*12 = 84

Finally, number of students = 22 + 7 = 29
Total age of the 29 students = total age of the 22 old students + total age
of the 7 new students = 346 + 84 = 430

So the present average = 

Hope you got it :)