There were an equal number of boys in Class P and Class Q. ⁴₅ of the students in Class P and ¹₄ of the students in Class Q are girls. If there are 33 more girls in Class P than in Class Q, what is the total number of students in Class P and Class Q?
Fraction of the students in Class P that are boys
= 1 - ⁴₅
=  ¹₅

Fraction of the students in Class Q that are boys
= 1 - ¹₄
= ³₄ 

The number of boys in Class P is equal to the number of boys in Class Q. LCM of 1 and 3 is 3. Make the numerators the same. 

 1x35x3 Class P = 34 Class Q 
 315 Class P = 34 Class Q

Number of boys in each class = 3 u

Total number of students in Class P = 15 u
Total number of students in Class Q = 4 u

Number of girls in Class P
= 15 u - 3 u
= 12 u

Number of girls in Class Q
= 4 u - 3 u
= 1 u

Number of more girls in Class P than Class Q
= 12 u - 1 u
= 11 u

11 u = 33

1 u = 33 ÷ 11 = 3

Total number of students
= 15 u + 4 u
= 19 u
= 19 x 3
= 57

Answer(s): 57