Question

A cricketer whose bowling average is 12.4 runs per wicket, takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets taken by him till the last match was:
A.64
B.72
C.80
D.85

Answer 1

Hint: We will assume the number of wickets taken by the cricketer as \[x\], then we will form equations and expressions for the average of the cricketer based on the condition given in the question. Then we can easily solve this equation and find the number of wickets taken by the cricketer.

Complete step-by-step answer:
Let us assume that the number of wickets take by the cricketer after the match is \[x\]. So, the number of wickets taken by the cricketer before this match would have been \[x - 5\]. Also the total number of runs conceded by the cricketer before the match would have been \[12.4(x - 5)\]. Thus, runs conceded by the cricketer after the match will be \[12.4(x - 5) + 26\].
On solving the above expression, we will get
 \[
  12.4(x - 5) + 26 \\
   = 12.4x - 62 + 26 \\
   = 12.4x - 36 \\
\]
Now, we have the total runs conceded by the cricketer after the match as \[12.4x - 36\] and the total number of wickets taken by the cricketer after the match as \[x\], thus his average will be \[\dfrac{{12.4x - 36}}{x}\].
It is given in the question, that the bowling average of the cricketer decreases by 0.4, thus his new average will be \[12.4 - 0.4 = 12\].
Now, we can equate the expression for bowling average with its value and get the value of \[x\].
On equating, we get
\[
   \Rightarrow \dfrac{{12.4x - 36}}{x} = 12 \\
   \Rightarrow 12.4x - 36 = 12x \\
   \Rightarrow 12.4x - 12x = 36 \\
   \Rightarrow 0.4x = 36 \\
   \Rightarrow x = 90 \\
\]
Thus, the total number of wickets taken by the cricketer after the match is 90, so wickets taken by him before the match would have been \[90 - 5 = 85\] wickets.
Hence, option (D) is the correct option.

Note: A higher bowling average indicates the cricketer is conceding more runs per wickets taken, indicating that his performance is not good.
In the above question, another way to solve it would be to assume the wickets taken by the bowler before the match as \[x\] and then solve accordingly.