The average test score of a group of students was 69 marks. After 3 students who scored an average of 87 marks joined the group, the average score of all the students became 75 marks. How many students were there in the group at first?
|
At first |
Joined |
In the end |
Number |
1 u |
3 |
1 u + 3 |
Value |
69 |
87 |
75 |
Total value |
69 u |
261 |
75 u + 225 |
Number of students at first = 1 u
Number of students in the end = 1 u + 3
Total test score at first
= 1 u x 69
= 69 u
Total test score for students who joined
= 3 x 87
= 261
Total test score in the end
= 75(1 u + 3)
= 75 u + 225
Total test score in the end is equal to sum of the total score at first and total score of the students who joined.
75 u + 225 = 69 u + 261
75 u - 69 u = 261 - 225
6 u = 36
1 u = 36 ÷ 6 = 6
Number of students at first
= 1 u
= 6
Answer(s): 6