The proportion of students in three classes is 3 : 4 : 5. If the number of students is increased by 20 in each class, then the proportion changes to 4 : 5 : 6. What is the initial number of students in the three classes taken together?

240

Classes -      I   :   II   :   III

Students      3  :   4    :    5

                   4  :   5    :    6

            __________________

                +20   +20     +20

Taking the first two ratios,

16r - 15r = (20 x 5) - (20 x 4)

⇒      r    = 20

Thus, the initial number of students = 3 x 20, 4 x 20, 5 x 20 

                                                    = 60, 80, 100

Total number of students = 60 + 80 + 100 = 240