Question

The average of runs of a cricket player of $10$ innings was $32$. How many runs must he make in his next innings so as to increase his average of runs by $4$?

• A. $4$
• B. $70$
• C. $76$
• D. $72$

Answer 1

The correct option is C $76$

let the $10$ innings runs be $a_1,a_2,...,a_{10}$

Given that average of $10$ innings is $32$

Therefore, $32=\frac{a_1+a_2+...+a_{10}}{10}$

$⟹a_1+a_2+...+a_{10}=320$ -------(1)

Let the next innings runs be $a_{11}$

The average is increased by $4$ with the next inning runs.

$⟹32+4=\frac{a_1+a_2+...+a_{10}+a_{11}}{11}$

$⟹a_1+a_2+...+a_{10}+a_{11}=36\times 11$

$⟹a_1+a_2+...+a_{10}+a_{11}=396$ -------(2)

substituting (1) in (2) we get

$320+a_{11}=396$

$⟹a_{11}=396-320$

$⟹a_{11}=76$

Therefore, the next innings rums should be $76$ to increase the average by $4$.