The Crockett Cricket Club awards its bowling trophy each year to the bowler who has the best average (computed by dividing the runs hit off the bowler by the wickets taken) over the whole season.
In 2009-10, Chester Chucker had an average of 50 runs per wicket for the first half of the season and an average of 25 runs per wicket for the second half of the season. On the other hand, Slim (Slow) Spin had a worse average in each half of the season than Chester. Slim’s two averages were 51 in the first half and 25.1 in the second.
(a) Give an example to show that Slim could end up with the Crockett Cricket Club bowling trophy for 2011-12?
(b) Can Chester ever win the trophy?
Solution
(a) Because both players had a better average in the second half of the season, Slim could have had a better overall average if he took more wickets in the second half of the season. Chester could have had figures of something like 100 runs for 2 wickets and 25 runs for 1 wicket to give him an average of 125/3 = 41.66. Slim's figures could have been 51 for 1 and 151 for 6 for a season long average of 202/7 = 28.85.
(b) Chester would have won if he and Slim had taken both taken the same number of wickets each in each half of the season.