Question

In a History examination, the average for the entire class was $80$ marks. If $10$% of the student 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 1

Answer: (C)

$75$

let the number of total students be x

then avg marks$=\frac{totalmarks}{x}$

$totalmarks=80x$

10% scored 95 that is $\frac{x}{10}$ scored 95

20% scored 90 that is$\frac{x}{5}$ scored 90

total marks of these 30% students is $\frac{95x}{10}+\frac{90x}{5}$

$=\frac{275x}{10}$

total marks of remaining students is $80x-\frac{275x}{10}$

$=\frac{525x}{10}$

number of remaining students are $x-\frac{x}{10}-\frac{x}{5}$

$=\frac{7x}{10}$

now average of remaining students is $\frac{totalmarks}{totalstudents}$

$=\frac{\frac{525x}{10}}{\frac{7x}{10}}$

$=75$