The average exam score of a group of pupils was 56 marks. After 5 pupils who scored an average of 67 marks joined the group, the average score of all the pupils became 61 marks. How many pupils were there in the group at first?
| |
At first |
Joined |
In the end |
| Number |
1 u |
5 |
1 u + 5 |
| Value |
56 |
67 |
61 |
| Total value |
56 u |
335 |
61 u + 305 |
Number of pupils at first = 1 u
Number of pupils in the end = 1 u + 5
Total exam score at first
= 1 u x 56
= 56 u
Total exam score for pupils who joined
= 5 x 67
= 335
Total exam score in the end
= 61(1 u + 5)
= 61 u + 305
Total exam score in the end is equal to sum of the total score at first and total score of the pupils who joined.
61 u + 305 = 56 u + 335
61 u - 56 u = 335 - 305
5 u = 30
1 u = 30 ÷ 5 = 6
Number of pupils at first
= 1 u
= 6
Answer(s): 6
