GATE 2021 CS-Set-2

Given Initial ratio : 3:13:6

Total number of students initially = 3x+13x+6x = 22x

From the given question, we can write 3x+18 = 15y —–I

                                   13x+18 = 35y—–II

                                   6x+18 = 21y——III

                      I – II => -10X = -20Y

                                    X=2Y——IV

                      Put IV in III => 6(2y) + 18 = 21y

                                       12y + 18 = 21y

                                       9y = 18

                                        y = 2 —–V

                      Substitute V in I => 3x + 18 = 30

                                           3x = 12

                                           x = 4

   Number of initial students = 22x = 22(4) = 88