The average test score of a group of students was 67 marks. After five students who scored an average of 75 marks left the group, the average score of the group became 65 marks. How many students were there at first?
| |
At first |
Left |
In the end |
| Number |
1 u + 5 |
5 |
1 u |
| Value |
67 |
75 |
65 |
| Total value |
67 u + 335 |
375 |
65 u |
Number of students in the end = 1 u
Number of students at first = 1 u + 3
Total test score in the end
= 1 u x 65
= 65 u
Total test score at first
= 67(1 u + 5)
= 67 u + 335
Total test score for students who left
= 5 x 75
= 375
Total test score at first is equal to sum of the total score in the end and total score of the students who left.
67 u + 335 = 65 u + 375
67 u - 65 u = 375 - 335
2 u = 40
1 u = 40 ÷ 2 = 20
Number of students at first
= 1 u + 5
= 20 + 5
= 25
Answer(s): 25
