Question 2

# The average marks obtained by a group of 16 students was 20. One student left the group as a result of which the average of the remaining students rose to 21. But another student joined,as a result of which the average marks of the group dropped a bit and became 20.5. What was the average marks obtained by the student who left and the one who joined?

Solution

Total marks obtained by all the 16 students = 16*20 = 320
Now, 1 student left.
Marks obtained by 15 students = 15*21 = 315
Hence, Marks obtained by the student who left = 320-315 = 5 marks
Now, 1 student joined.
Marks obtained by 16 students = 16*20.5 = 328
Hence, Marks obtained by newly joined student = 328-315 = 13 marks.
Therefore, Required average = $$\dfrac{5+13}{2} = \dfrac{18}{2} = 9$$

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