A school has 10 classes with the same number of students in each class. One day, the weather was bad and many students were absent. 3 classes were half full, 5 class were 3/4 full and 2 classes were 1/6 empty. A total of 74 students were absent. What is the total number of students in this school?

Let x = number of students in each class.

Then total number of students in school. is = 10x

If 3 classes are half full then we have 3x/2 students absent.

If 5 classes are 3/4 full that means that (1/4)*5x students are absent.

If 2 classes are 1/6 empty that means that (1/6)*2x students are absent.

Now we are told that

(3x/2) + (1/4)*5x + (1/6)*2x = 74

or,(3x/2) + (5x/4) + (x/3) = 74

or,18x + 15x + 4x = 888

or,7x = 280

x = 24 

number of students in each class is 24

number of student in this school = 10x

                                = 10*24 = 240

ans: 240