Question

A cricketer given $12.4$ runs per wicket.He gives $26$ runs and takes $5$ wicket in a match after which his average become $12$ per wickets. How many wickets had been taken till the last match?

Answer 1

Average run per wicket $=12.4$

LEt no. of wickets taken before last amtch$=x$

$\therefore \frac{Totalruns}{no.ofwicket}=12.4$

Total runs before last match$=12.4\times x$

In last match, he takes $=5$ wickets

In last match he gives$=26$ runs

$\therefore$ Average run per wicket become$=12$

According to question

$\frac{12.4\times x+26}{x+5}=12\Rightarrow 12.4x+26=12x+60\Rightarrow 12.4x-12x=60-26\Rightarrow 0.4x=34\Rightarrow x=\frac{34}{0.4}=\frac{340}{4}\Rightarrow x=85$

Hence the cricketer takes $=x+5\Rightarrow 85+5=90$

$90$ wickets