Question

only say me the answer of the question.​

Answer 1

Correct question.

Rank is in descending order. Since it is insufficient information, we cannot find the score of the 5th ranker. Instead can find the score of the 6th ranker.

Understanding the problem.

We are given the average of a whole class consisting of 10 students and the average of the top 6 students and 5 bottom students.

• Average- Whole class: 41
• Average- Top 6: 45
• Average- Bottom 5: 36

Since the average score comes from the sum of scores, we can find it inversely. Then can think of adding the marks of the top 6 and bottom 5, then subtracting the sum of each score.

Solution.

Let's begin with "What is the sum of the scores of the top 5 students and 5 bottom students?" The answer is the sum of all students' scores. Since we are given it, we can solve our problem.

Let the marks of each student be $x_{i}$, where $i$ is the rank of each student in descending order.

$\dfrac{x_{1}+x_{2}+...+x_{10}}{10}=41\text{\ [The average of 10 students.]}$

$\dfrac{x_{1}+x_{2}+...+x_{6}}{6}=45 \text{\ [The average of the top 6.]}$

$\dfrac{x_{6}+x_{7}+...+x_{10}}{5}=36 \text{\ [The average of the bottom 5.]}$

$\implies x_{1}+x_{2}+...+x_{10}=410$ …$\text{[Equation 1]}$

$\implies x_{1}+x_{2}+...+x_{6}=270$ …$\text{[Equation 2]}$

$\implies x_{6}+x_{7}+...+x_{10}=180$ …$\text{[Equation 3]}$

Adding $\text{[Equation 2]}$ and $\text{[Equation 3]}$ we obtain $(x_{1}+x_{2}+...+x_{10})+x_{6}=450$.

By the subtraction of it and $\text{[Equation 1]}$ we obtain $x_{6}=40$. Hence the score of the 6th ranker is $40$ marks.