The average test score of a group of pupils was 69 marks. After 6 pupils who scored an average of 78 marks joined the group, the average score of all the pupils became 72 marks. How many pupils were there in the group at first?
| |
At first |
Joined |
In the end |
| Number |
1 u |
6 |
1 u + 6 |
| Value |
69 |
78 |
72 |
| Total value |
69 u |
468 |
72 u + 432 |
Number of pupils at first = 1 u
Number of pupils in the end = 1 u + 6
Total test score at first
= 1 u x 69
= 69 u
Total test score for pupils who joined
= 6 x 78
= 468
Total test score in the end
= 72(1 u + 6)
= 72 u + 432
Total test score in the end is equal to sum of the total score at first and total score of the pupils who joined.
72 u + 432 = 69 u + 468
72 u - 69 u = 468 - 432
3 u = 36
1 u = 36 ÷ 3 = 12
Number of pupils at first
= 1 u
= 12
Answer(s): 12
