Let the original strength of the class be x

 Average age of x students = 42

∴ Sum of age of x students = 42x years

When, 12 students join the class, then number of students in the class = x + 12

Average of 12 new student’s age = 30yrs

∴ Sum of age of 12 students = 30 × 12 = 360 years

∴ Total sum of age of (x + 12) students = 42x + 360 years

∴ Average of (x+ 12) student’s age = $(\frac{{42{\rm{x\;}} + {\rm{\;}}360{\rm{\;}}}}{{{\rm{x\;}} + {\rm{\;}}12}})$

Given,

After the joining of 12 new students in the class, average age decrease by 8 years

$(\Rightarrow \;\frac{{42{\rm{x\;}} + {\rm{\;}}360{\rm{\;}}}}{{{\rm{x\;}} + {\rm{\;}}12}}\; = \;42 - 8)$

⇒ 42x + 360 = 34x + 408

⇒ 8x = 48

⇒ x = 6

∴ The original strength of the class was 6 students