Question

# A man whose bowling average is $12.4$ takes $5$ wickets for $26$ runs and thereby decreases his average by $0.4$. What is the number of wickets taken by him before his last match?

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Solution

## Let the number of wickets taken by him before the match be $x$.The bowling average is given to be $12.4$.Total runs $=12.4x$The runs scored including this match is given by $12.4x+26$ with the average of $12$.$\frac{\left(12.4x+26\right)}{x+5}=12\phantom{\rule{0ex}{0ex}}12.4x+26=12x+60\phantom{\rule{0ex}{0ex}}12.4x-12x=60-26\phantom{\rule{0ex}{0ex}}0.4x=34\phantom{\rule{0ex}{0ex}}\therefore x=85wickets$Hence, $85$ wickets are taken by the man before his last match.

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