A bowler gives 16.2 runs per wicket. He gives 32 runs and takes 8 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?

Bowling average = (total runs conceded)/(total wicket taken ) Let the total number of wickets be x Then, bowling average = 16.2 Runs conceded = 16.2 x Now, (16.2 x + 32)/(x + 8)= 15.4 16.2 x + 32 = 15.4 (x + 8) 16.2 x + 32 = 15.4 x + 123.2 0.8 x = 123.2 - 32 x = 91.2/0.8 = 114 Alternate method: Using Allegation method, Average rate before last match Average in last match 16.2 32/8 = 4 Net Average = 15.4 Number of wickets before last match wickets in last match 11.4 : 0.8 114 : 8 Hence number of wickets before last match = 114