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Question

The average of ten students marks are 47. If 11th student's marks are also included, then the average of eleven students marks becomes 45. Find the marks of 11th student.

A
35
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B
25
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C
45
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D
40
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Solution

The correct option is B 25
Let the 10 students marks be a1,a2,...,a10

Given that average of 10 students marks is 47

Therefore, 47=a1+a2+...+a1010

a1+a2+...+a10=470 -------(1)

Let the 11th student marks be a11

Given that average of 11 students is 45

Therefore, 45=a1+a2+...+a10+a1111

a1+a2+...+a10+a11=495 -----(2)

substituting (1) in (2) we get

470+a11=495

a11=495470=25

Therefore, the 11th student marks is 25

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