Question

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.
A. 0
B. 45
C. 50
D. 47.5

Answer 1

Hint: Let the marks scored by the ${11^{th}}$ candidate be $x$. First, calculate the total marks scored by the 22 candidates then, find the total marks scored by the first 10 candidates and total marks scored by the last eleven candidates.

Complete Step by Step Solution:
In the question, we have been given that the average marks scored by the 22 candidates are 45.
Let the marks scored by the ${11^{th}}$ candidate be $x$.
We are given the question that the average marks of the first ten candidates are 55 and the last eleven candidates are 40.
We are given that the average marks scored by 22 candidates in an examination are 45. Therefore, total marks scored by 22 candidates are $22 \times 45 = 990$.
Now, calculating the total marks scored by the first 10 candidates –
$ \Rightarrow 10 \times 55 = 550$
Hence, the first 10 candidates scored 550 marks.
We are also given that the average marks of the last eleven candidates are 40. Therefore, the total marks of the last eleven candidates are –
$ \Rightarrow 11 \times 40 = 440$
Hence, the last eleven candidates scored 440 marks.
We know that –
Total marks scored by the candidates = Total marks of first 10 candidates + Mark of ${11^{th}}$ candidate + Total marks of last 11 candidates.
Putting values, we get –
$
   \Rightarrow 990 = 550 + x + 440 \\
   \Rightarrow x = 990 - 990 \\
  \therefore x = 0 \\
 $

Hence, the mark of ${11^{th}}$ candidate is 0 and the correct option is (A).

Note: The average of the data can be given by formula - $\dfrac{{{S_O}}}{N}$ where ${S_O}$ is the sum of observation and $N$ is the number of observations. Then, the sum of observations will be calculated by multiplying the average with the number of observations.