Question

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 1

Answer: (C)

75

Let $n$ be the total number of students

Average marks $=80=\frac{totalmarks}{n}$

$10\%$ has scored $95$

M1 $=(\frac{10}{100}\times n)\times 95=\frac{95n}{10}$ (total marks of $10\%$ of students)

$20\%$ has scored 90

M2 $=(\frac{20}{100}\times n)\times 90=\frac{180n}{10}$

rest $70\%$ $100-10-20$ scores $x$

M3 $=(\frac{70}{100}\times n)\times x=\frac{7nx}{10}$

total marks $=M1+M2+M3=\left(\frac{275+7x}{10}\right)n$

$⟹80=\frac{total}{n}=\frac{275+7x}{10}$

$⟹800=275+7x$

$⟹x=75$

$\therefore$ rest of the class has scored $75$