There were an equal number of girls in Class X and Class Y. ⁴₅ of the students in Class X and ¹₄ of the students in Class Y are boys. If there are 55 more boys in Class X than in Class Y, what is the total number of students in Class X and Class Y?
Fraction of the students in Class X that are girls
= 1 - ⁴₅
=  ¹₅

Fraction of the students in Class Y that are girls
= 1 - ¹₄
= ³₄ 

The number of girls in Class X is equal to the number of girls in Class Y. LCM of 1 and 3 is 3. Make the numerators the same. 

 1x35x3 Class X = 34 Class Y 
 315 Class X = 34 Class Y

Number of girls in each class = 3 u

Total number of students in Class X = 15 u
Total number of students in Class Y = 4 u

Number of boys in Class X
= 15 u - 3 u
= 12 u

Number of boys in Class Y
= 4 u - 3 u
= 1 u

Number of more boys in Class X than Class Y
= 12 u - 1 u
= 11 u

11 u = 55

1 u = 55 ÷ 11 = 5

Total number of students
= 15 u + 4 u
= 19 u
= 19 x 5
= 95

Answer(s): 95