The average exam score of a group of students was 58 marks. After 3 students who scored an average of 69 marks joined the group, the average score of all the students became 61 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 |
58 |
69 |
61 |
| Total value |
58 u |
207 |
61 u + 183 |
Number of students at first = 1 u
Number of students in the end = 1 u + 3
Total exam score at first
= 1 u x 58
= 58 u
Total exam score for students who joined
= 3 x 69
= 207
Total exam score in the end
= 61(1 u + 3)
= 61 u + 183
Total exam score in the end is equal to sum of the total score at first and total score of the students who joined.
61 u + 183 = 58 u + 207
61 u - 58 u = 207 - 183
3 u = 24
1 u = 24 ÷ 3 = 8
Number of students at first
= 1 u
= 8
Answer(s): 8
