The average exam score of a group of pupils was 67 marks. After 6 pupils who scored an average of 83 marks joined the group, the average score of all the pupils became 73 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 |
67 |
83 |
73 |
| Total value |
67 u |
498 |
73 u + 438 |
Number of pupils at first = 1 u
Number of pupils in the end = 1 u + 6
Total exam score at first
= 1 u x 67
= 67 u
Total exam score for pupils who joined
= 6 x 83
= 498
Total exam score in the end
= 73(1 u + 6)
= 73 u + 438
Total exam score in the end is equal to sum of the total score at first and total score of the pupils who joined.
73 u + 438 = 67 u + 498
73 u - 67 u = 498 - 438
6 u = 60
1 u = 60 ÷ 6 = 10
Number of pupils at first
= 1 u
= 10
Answer(s): 10
