Question 256593
Let the number of boys be 19x
Then the number of girls is 17x
Total number of students = 19x+17x = 36x
Given total 36x = 1908
              x = 1908/36
              x = 53
Therefore the number of boys = 19*53 = 1007
Then the number of girls = 17*53 = 901

Another Method
Let the number of boys be x
And the number of girls is y
Given,  x/y = 19/17
        17x = 19y
        17x-19y = 0  ...(1)
Next,    
Total number of students is x+y = 1908  ...(2)
(2)*19 =>  19x+19y = 36252 ...(3)
(2)+(3) => 36x = 36252
             x = 36252/36
             x = 1007

Therefore the number of boys = 19*53 = 1007
Then the number of girls = 1908-1007 = 901