The average test score of a group of pupils was 78 marks. After four pupils who scored an average of 91 marks left the group, the average score of the group became 74 marks. How many pupils were there at first?
| |
At first |
Left |
In the end |
| Number |
1 u + 4 |
4 |
1 u |
| Value |
78 |
91 |
74 |
| Total value |
78 u + 312 |
364 |
74 u |
Number of pupils in the end = 1 u
Number of pupils at first = 1 u + 3
Total test score in the end
= 1 u x 74
= 74 u
Total test score at first
= 78(1 u + 4)
= 78 u + 312
Total test score for pupils who left
= 4 x 91
= 364
Total test score at first is equal to sum of the total score in the end and total score of the students who left.
78 u + 312 = 74 u + 364
78 u - 74 u = 364 - 312
4 u = 52
1 u = 52 ÷ 4 = 13
Number of pupils at first
= 1 u + 4
= 13 + 4
= 17
Answer(s): 17
