A bowler gives 16.2 runs per wicket. He gives 40 runs and takes 4 wickets in a last match after which his average becomes 15.4 runs per wicket. How many wickets had been taken by him before the last match?

A bowler gives 16.2 runs per wicket. He gives 40 runs and takes 4 wickets in a last match after which his average becomes 15.4 runs per wicket. How many wickets had been taken by him before the last match? Correct Answer 27

GIVEN:

Bowler’s old average = 16.2

Bowler’s new Average = 15.4

FORMULA USED:

Bowling average = Total runs conceded/Total wicket taken

CALCULATION:

Let the total number of wickets be x

Then, bowling average = 16.2

Runs conceded = 16.2 x

Now, (16.2 x + 40)/(x +  4) = 15.4 

16.2 x + 40 = 15.4 (x + 4)

16.2 x + 40 = 15.4 x + 61.6

0.8 x = 61.6 – 40

x = 21.6/0.8 = 27

Alternate method:

By Allegation:

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Hence total number of wickets taken before last match = 27