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 $40$.
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