The average marks obtained by 60 students in a computer examination is 18. If the average marks of passed students is 20 and that of the failed students is 8, what is the number of students who passed the examination?Options50526645
Question
The average marks obtained by 60 students in a computer examination is 18. If the average marks of passed students is 20 and that of the failed students is 8, what is the number of students who passed the examination?Options50526645
Solution
To solve this problem, we can use the concept of weighted averages.
Step 1: Let's denote the number of students who passed the exam as P and the number of students who failed as F. We know that P + F = 60.
Step 2: We also know that the average mark of all students is 18, which is the total marks divided by the total number of students. This can be written as (20P + 8F) / 60 = 18.
Step 3: Simplifying the above equation gives 20P + 8F = 1080.
Step 4: We can also express F as 60 - P from step 1. Substituting this into the equation from step 3 gives 20P + 8(60 - P) = 1080.
Step 5: Simplifying this equation gives 20P + 480 - 8P = 1080, which simplifies further to 12P = 600.
Step 6: Solving for P gives P = 600 / 12 = 50.
So, 50 students passed the examination.
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