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% of a mean score of 31. The mean score of remaining 55% is
Options:	A) 40.8 approx	B) 45.3 approx	C) 51.4 approx	D) 53.8 approx	E) None
Sol.   Let the required mean score be x. Then,   20 × 80 + 25 × 31 + 55 × x = 52 × 100   ⇔ 1600 + 775 + 55x = 5200   ⇔ 55x = 2825   ⇔ x = 565 / 11 = 51.4.   Answer 51.4 approx
<result>C</result>
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% of a mean score of 31. The mean score of remaining 55% is