There were an equal number of girls in Class Q and Class R. ²₃ of the pupils in Class Q and ¹₅ of the pupils in Class R are boys. If there are 42 more boys in Class Q than in Class R, what is the total number of pupils in Class Q and Class R?
Fraction of the pupils in Class Q that are girls
= 1 - ²₃
=  ¹₃

Fraction of the pupils in Class R that are girls
= 1 - ¹₅
= ⁴₅ 

The number of girls in Class Q is equal to the number of girls in Class R. LCM of 1 and 4 is 4. Make the numerators the same. 

 1x43x4 Class Q = 45 Class R 
 412 Class Q = 45 Class R

Number of girls in each class = 4 u

Total number of pupils in Class Q = 12 u
Total number of pupils in Class R = 5 u

Number of boys in Class Q
= 12 u - 4 u
= 8 u

Number of boys in Class R
= 5 u - 4 u
= 1 u

Number of more boys in Class Q than Class R
= 8 u - 1 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

Total number of pupils
= 12 u + 5 u
= 17 u
= 17 x 6
= 102

Answer(s): 102