Question

A batsman in his ${16}^{th}$ innings makes a score of $70$ and thereby increases his average by $2$ runs. If he had never been 'not out', then his average after ${16}^{th}$ innings is :

• A. $36$
• B. $38$
• C. $40$
• D. $42$
• E. $44$

Answer 1

Answer: (C)

$40$

Let average of $15$ innings be $y.$

$\therefore$ $\frac{{\text{Total score (upto 15}}^{th}\text{innings)}}{15}=y$

$\Rightarrow {\text{Total score (upto 15}}^{th}\text{innings)}=15y$

According to the given condition, we have

$y+2=\frac{15y+70}{16}$

$\Rightarrow 16y+32=15y+70$

$\Rightarrow y=38$

Therefore, average after $16$ innings $=\frac{15\times 38+70}{16}$
$=\frac{570+70}{16}=\frac{640}{16}=40$