The average marks obtained by 180 students in an examination is 50. If the average marks of passed students is 80 and that of the failed students is 40, then what is the number of students who failed the examination ?

Number of unsuccessful students = x

∴ Number of successful students = 180 – x

According to the question,

$frac{x imes 40+(180-x) imes 80}{180}=50$

$Rightarrow 4 x+(180-x) imes 8=50 imes 18 quad Rightarrow x+(180-$

$x) imes 2=25 imes 9$

$Rightarrow x+360-2 x=225$

$Rightarrow x=360-225=135$