The average marks of $10$ students is $41$. If the average marks of the top $6$ and bottom $5$ rankers are $45$ and $36$ respectively, how much did the $5^{th}$ ranker score?

Given: The average marks of $10$ students is $41$. If the average marks of the top $6$ and bottom $5$ rankers are $45$ and $36$ respectively.

To do: To find the  $5^{th}$ ranker score.

Solution:

As given, The average marks of $10$ students is $41$.

As known, $average=\frac{Total\ marks\ of\ the\ students}{No.\ of\ students}$

Therefore, total marks of the student$=(average)\times (no.\ of\ students)$

$=41\times10$

$=410$

Similarly, Total marks of the top $6$ rankers$=6\times45=270$

And total marks of the bottom $5$ rankers$=5\times36=180$

Total marks of top $6$ rankers and bottom $5$ rankers$=270+180=450$

Therefore $5^{th}$ ranker score$=450-410=40$

Thus, $5^{th}$ ranker score is $40$.