Question

In a class of 100 students, the average marks scored was 31. If the students who passed obtained an average of 42 marks and those who failed obtained an average of 20 marks, how many students passed the exam?

• A. 40
• B. 55
• C. 50
• D. 45

Answer 1

The correct option is C 50

Let the number of passed students $=x$
Number of failed students
$=\text{Total – Passed students}$

Number of failed students $=100-x$

Average of the entire class
$=\frac{\text{Total marks scored}}{\text{Number of students}}$

$⟹\frac{\text{Total marks scored}}{100}=31$
$⟹\text{Total marks scored}=31\times 100$
$⟹\text{Total marks scored}=3100$

Average of the passed students
$=\frac{\text{Total marks by the passed students}}{\text{Number of passed students}}$

$⟹\frac{\text{Marks by the passed students}}{x}=42$
$⟹\text{Marks by the passed students}=42\times x$
$=42x$

Average of the failed students
$=\frac{\text{Total marks by failed students}}{\text{Number of failed students}}$

$⟹\frac{\text{Marks by failed students}}{100-x}=20$
$⟹\text{Marks by failed students}=20\times (100-x)$
$=2000-20x$

Total marks scored by the passed students + Total marks scored by failed students = Total marks scored by all students

$42x+2000-20x=3100$
$42x-20x=3100-2000$
$22x=1100$

$x=\frac{1100}{22}$

$x=50$

Therefore, 50 students passed the exam.