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The average marks scored by 22 candidates in an examination are 45. The average marks of the first ten are 55 and the last eleven are 40. Find the number of marks which is obtained by $11^{th}$ candidate.

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Detailed Solution

Given that the average marks scored by 22 candidates in an examination = 45.
So, the total marks scored by 22 candidates are

\Rightarrow 22 \times 45 = 990

Average = \frac{sum of observation}{number of observations} \Rightarrow Average \times number of observations = sum of observation

Again given, the average marks of the first ten = 55.
So, the total marks scored by the first 10 candidates

\Rightarrow 10 \times 55 = 550

The average marks of the last eleven = 40.
So, the total marks of the last eleven candidates are:

\Rightarrow 11 \times 40 = 440

And, let the marks scored by the

11^{th}

candidate be

x

.
Now, we know that
The total marks scored = Total marks of the first 10 candidates + Mark of

11^{th}

+ Total marks of the last 11 candidates

\Rightarrow 990 = 550 + x + 440

\Rightarrow x = 990 - 990

\Rightarrow x = 0

Thus, the number of marks which is obtained by

11^{th}

the candidate is 0.

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