Question

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

• A. $35$
• B. $25$
• C. $45$
• D. $40$

Answer 1

The correct option is B $25$

Let the $10$ students marks be $a_1,a_2,...,a_{10}$

Given that average of $10$ students marks is $47$

Therefore, $47=\frac{a_1+a_2+...+a_{10}}{10}$

$⟹a_1+a_2+...+a_{10}=470$ -------(1)

Let the ${11}^{th}$ student marks be $a_{11}$

Given that average of $11$ students is $45$

Therefore, $45=\frac{a_1+a_2+...+a_{10}+a_{11}}{11}$

$⟹a_1+a_2+...+a_{10}+a_{11}=495$ -----(2)

substituting (1) in (2) we get

$470+a_{11}=495$

$⟹a_{11}=495-470=25$

Therefore, the ${11}^{th}$ student marks is $25$