The average test score of a group of students was 61 marks. After 6 students who scored an average of 79 marks joined the group, the average score of all the students became 67 marks. How many students were there in the group at first?
| |
At first |
Joined |
In the end |
| Number |
1 u |
6 |
1 u + 6 |
| Value |
61 |
79 |
67 |
| Total value |
61 u |
474 |
67 u + 402 |
Number of students at first = 1 u
Number of students in the end = 1 u + 6
Total test score at first
= 1 u x 61
= 61 u
Total test score for students who joined
= 6 x 79
= 474
Total test score in the end
= 67(1 u + 6)
= 67 u + 402
Total test score in the end is equal to sum of the total score at first and total score of the students who joined.
67 u + 402 = 61 u + 474
67 u - 61 u = 474 - 402
6 u = 72
1 u = 72 ÷ 6 = 12
Number of students at first
= 1 u
= 12
Answer(s): 12
