The average marks obtained by 150 students in a certain examination is 50. If the average marks of the passed students are 54 and that of the students who failed are 30, then what will be the number of the students who failed?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 25
Concept USed:
Sum of terms = Average of terms × Number of terms
Explanation:
Let the number of students failed be x.
So the number of students who passed is (150 - x)
According to the given question,
The sum of marks obtained by 150 students = 50 × 150 = 7500
The sum of marks obtained by passed students = 54 × (150 - x)
Te sum of marks obtained by failed students = 30 × x = 30x
Now, 54 × (150 - x) + 30x = 7500
⇒ 8100 - 54x + 30x = 7500
⇒ 8100 - 24x = 7500
⇒ 24x = 600
⇒ x = 25
Hence the number of students who failed is 25.