Question : The average mark obtained by 180 students in an examination is 50. If the average mark of passed students is 80 and that of the failed students is 40, then what is the number of students who failed the examination?
Option 1: 90
Option 2: 135
Option 3: 100
Option 4: 45
Correct Answer: 135
Solution : Let the number of failed students be $x$. Total marks obtained = 180 × 50 = 9000 According to the question, 40$x$ + (180 – $x$) × 80 = 9000 ⇒ 40$x$ + 14400 – 80$x$ = 9000 ⇒ 40$x$ = 5400 ⇒ $x$ = 135 Hence, the correct answer is 135.
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