In a History examination, the average for the entire class was 80 marks. If 10\% of the students scored 95 marks and 20\% scored 90 marks, what was the average marks of the remaining students of the class?
(a)65.5
(b)72.5
(c)75
(d)85
Answer
Answer (as printed): C
Explanation
Let the number of students in the class be 100 and let the required average be $x$. Then, $(10 \times 95)+(20 \times 90)+(70 \times x)=(100 \times 80)$ $$\Rightarrow \quad 70 x=8000-(950+1800)=5250 \Leftrightarrow x=75 .$$
Explanation as extracted from the printed page; notation may be imperfect.