The arithmetical mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25%, a mean score of 31. The mean score of remaining 55% is

Let the total number of students be 100.
Also, let the mean score = N
According to the question,
20 x 80 + 25 x 31 + (100 - 20 - 25) x N = 100 x 52
⇒ 1600 + 775 + (55) x N = 5200
⇒ 55N = 5200 - 1600 - 775
∴ N = 2825/55 = 51.36 = 51.4%
So, mean score of remaining 55% is 51.4%