A cricketer has a bowling average of 14.2 runs per wicket. He is not able to perform well in the last match due to fever and hence takes only 6 wickets for 34 runs, thereby decreasing his average by 0.4. Find the total number of wickets taken by him till the last match.
The bowling average is found by the total number of runs taken per wicket ATQ, let the total number of wickets taken (excluding the last match) be x
The total number of runs scored will be 14.2x
Now, including the last match statistics, we get,
Total number of wickets = x + 6
Total number of runs scored = 14.2x + 34
Hence, The bowling average can be given by,
(14.2x + 34) ÷ (x + 6) = 13.8
⇒ 14.2x + 34 = 13.8x + 82.8
⇒ 0.4x = 48.8
⇒ x = 122
∴ the number of wickets till last match will be = 122 + 6 = 128