Question : The average mark obtained by 120 students in an examination is 50. If the average mark of passed students is 70 and the average mark of the failed students is 30, then what is the number of students who passed the examination?
Option 1: 100
Option 2: 60
Option 3: 80
Option 4: 40
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Correct Answer: 60
Solution : Given, Average marks of 120 students = 50 Average marks of passed students = 70 Average marks of failed students = 30 We know, Total marks = Number of students $\times$ Average marks ⇒ Total marks of 120 students = 120$\times$50 = 6000 Let the number of students who passed be $x$. Total marks of passed students + Total marks of failed students = Total marks of all students ⇒ $70x + 30(120-x) = 6000$ ⇒ $40x = 2400$ ⇒ $x = \frac{2400}{40}$ ⇒ $x = 60$ Hence, the correct answer is 60.
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