Let the total number of students = N

So N are taking chemistry

The trick here is "the remaining students".  That is NOT 
 of the total number of students!  It is only
 of the students that remain after the N
chemistry students have been subtracted from N, which is 
N - N or N.  Therefore  of N 
is N.  So the number talking physics is N.

and the rest are taking biology. 

"The rest" is found by subtracting the N taking
chemistry and the N taking physics from N:

N - (N + N) = N - N = N are taking biology 

So we set N = 66

Multiply through by 5

2N = 330
 N = 165

Edwin