Question : A cricketer whose bowling average was 12.4 runs per wicket takes 5 wickets for 22 runs in a match, thereby decreasing his average by 0.4. The number of wickets taken by him before this match was:
Option 1: 78
Option 2: 87
Option 3: 95
Option 4: 105
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Correct Answer: 95
Solution :
Given: Bowling average is 12.4.
Let the number of wickets taken by him before the match be $x$.
The total runs = $12.4x$
The runs scored including this match are given by $12.4x + 22$ with an average of 12.
According to the question,
⇒ $\frac{12.4x+22}{x+5}=12$
⇒ $12.4x + 22 = 12x + 60$
⇒ $0.4x = 38$
$\therefore x=95$
Hence, the correct answer is 95.
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