1.  The arithmetic 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 :
A. 45
B. 50
C. 51.4 approx
D. 54.6 approx

Answer: Option C

Explanation:

Let the required mean score be X. Then,

 20 x 80 + 25 x 31 + 55 x X = 52 x 100

<=> 1600 + 775 + 55X = 5200

<=> 55X = 2825

<=> X = (565/11) = 51.4