Let the three classes have $3x$, $13x$ and $6x$ students respectively. $18$ students are added in each class.
After that $3x+18,13x+18$ and $6x+18$ are the number of students in each class.
Given, $3x+18: 13x+18 : 6x+18 = 15:35:21$
$\implies \frac{3x+18}{6x+18}=\frac{15}{21}$
$\implies \frac{x + 6}{2x + 6} = \frac{5}{7}$
$\implies 7x + 42 = 10x + 30$
$\implies 3x = 12$
$\implies x = 4$
So, the total number of students in all the three classes, in the beginning, $=3*4+13*4+6*4=88.$
Option (C) is the correct answer.