The average test score of a group of students was 64 marks. After 6 students who scored an average of 82 marks joined the group, the average score of all the students became 73 marks. How many students were there in the group at first?
| |
At first |
Joined |
In the end |
| Number |
1 u |
6 |
1 u + 6 |
| Value |
64 |
82 |
73 |
| Total value |
64 u |
492 |
73 u + 438 |
Number of students at first = 1 u
Number of students in the end = 1 u + 6
Total test score at first
= 1 u x 64
= 64 u
Total test score for students who joined
= 6 x 82
= 492
Total test score in the end
= 73(1 u + 6)
= 73 u + 438
Total test score in the end is equal to sum of the total score at first and total score of the students who joined.
73 u + 438 = 64 u + 492
73 u - 64 u = 492 - 438
9 u = 54
1 u = 54 ÷ 9 = 6
Number of students at first
= 1 u
= 6
Answer(s): 6
