The average quiz score of a group of pupils was 57 marks. After 6 pupils who scored an average of 75 marks joined the group, the average score of all the pupils became 63 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 |
57 |
75 |
63 |
| Total value |
57 u |
450 |
63 u + 378 |
Number of pupils at first = 1 u
Number of pupils in the end = 1 u + 6
Total quiz score at first
= 1 u x 57
= 57 u
Total quiz score for pupils who joined
= 6 x 75
= 450
Total quiz score in the end
= 63(1 u + 6)
= 63 u + 378
Total quiz score in the end is equal to sum of the total score at first and total score of the pupils who joined.
63 u + 378 = 57 u + 450
63 u - 57 u = 450 - 378
6 u = 72
1 u = 72 ÷ 6 = 12
Number of pupils at first
= 1 u
= 12
Answer(s): 12
