Question

A batsman by scoring 68 runs in his ${20}^{th}$ inning improves his average by 2 runs. His average for all 20 innings is

• A. $28$
• B. $30$
• C. $32$
• D. $34$

Answer 1

Answer: (B)

$30$

let the $19$ innings runs be $a_1,a_2,...,a_{19}$

let the average of $19$ innings be $\overline{x}$

Therefore, $\overline{x}=\frac{a_1+a_2+...+a_{19}}{19}$

$⟹a_1+a_2+...+a_{19}=19\overline{x}$ -------(1)

Given that ${20}^{th}$ inning runs is $68$

The average is increased by $2$ with the ${20}^{th}$ inning runs.

$⟹\overline{x}+2=\frac{a_1+a_2+...+a_{19}+a_{20}}{20}$

$⟹a_1+a_2+...+a_{19}+68=20\overline{x}+40$

$⟹a_1+a_2+...+a_{19}+28=20\overline{x}$ -------(2)

substituting (1) in (2) we get

$19\overline{x}+28=20\overline{x}$

$⟹\overline{x}=28$

Therefore, the $20$ innings average is $\overline{x}+2=28+2=30$