The students of three classes are in the ratio 4 : 6 : 9. If 12 students are increased in each class the ratio changes to 7 : 9 : 12. Then the total number of students in the three classes before the increase is = ?

Let class A, B and C then Number of student ratio in A : B : C = 4 : 6 : 9 = 4x : 6x : 9x
And Now 12 Student join in all Class and their ratio become
A : B : C = 7 : 9 : 12 = 7x : 9x : 12x

∴ in A → 7x - 4x = 12 , In B → 9x - 6x = 12 and In C →12x - 9x = 12
i.e. x = 4
Total number of Student before new student are
= 4 × 4 + 6 × 4 + 9 × 4
= 76