Question

The average of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured an average score of $80$ and the dullest $25\%$ secured an average score of $31$. Then the average score of remaining $55\%$ is:

• A. $45$
• B. $50$
• C. $51.4$ approx
• D. $54.6$ approx

Answer 1

Answer: (C)

$51.4$ approx

Given that $20\%$ of the students secured an average score of $80$

Let the total number of students be $x$

Therefore, $80=\frac{\text{sum of the scores of the 20\% students}}{0.2x}$

$\text{sum of the scores of the 20\% students}=16x$ ------(1)

Given that $25\%$ of the students secured an average score of $31$

Therefore, $31=\frac{\text{sum of the scores of the 25\% students}}{0.25x}$

$\text{sum of the scores of the 25\% students}=7.75x$ ------(2)

Given that the average of score of the total number of students is $52$

Therefore, $52=\frac{\text{sum of the scores of 20\% students + sum of the scores of 25\% students + remaining 55\% students}}{x}$ ------(3)

substituting (1) and (2) in (3) we get

$16x+7.75x+\text{sum of the scores of remaining 55\% students}=52x$

$⟹23.75x+\text{sum of the scores of remaining 55\% students}=52x$

$⟹\text{sum of the scores of remaining 55\% students}=28.25x$ -----(4)

Therefore, the average score of remaining $55\%$ students is $\frac{\text{sum of the 55\% students scores}}{0.55x}$

$=\frac{28.25x}{0.55x}=51.36=51.4$ approx.