Question

What will be the number of wickets taken by the cricketer till the last match if his bowling average is 12.4 runs per wicket, takes 5 wickets for 26 runs and so decreases his average by 0.4?
A. 64
B. 72
C. 80
D. 85

Answer 1

Hint: Let us consider the number of wickets taken till the last match be $x$ in order to calculate the number of wickets of the cricketer till the last match. Then, we can compute the total average runs per wickets using the formula of average = $\dfrac{{{\text{total number of runs}}}}{{{\text{total wickets}}}}$ to find $x$.

Complete Step by Step Solution:
Let the number of wickets taken till the last match by cricketer be $x$ and let the number of runs scored be $y$. Therefore, the bowling average can be calculated by –
$
   \Rightarrow \dfrac{y}{x} = 12.4 \\
   \Rightarrow y = 12.4x \\
 $
In the question, it is given that, the average is reduced by 0.4 adding 26 runs and 5 wickets. So, the average will be –
$ \Rightarrow {\text{Average}} = \dfrac{{{\text{total runs}}}}{{{\text{total wickets}}}}$
Putting values in the above formula, we get –
$
   \Rightarrow {\text{Average}} = \dfrac{{12.4x + 26}}{{x + 5}} = 12.4 - 0.4 \\
   \Rightarrow 12x + 60 = 12.4x + 26 \\
   \Rightarrow 0.4x = 34 \\
   \Rightarrow x = 85 \\
 $
Hence, the value of $x$ is $85$ so, the number of wickets taken by the cricketer till the last match is 85.

Therefore, the correct option is (D).

Note:
These types of questions require careful observations of what is given on the question. We need to establish the relationship between the given average and the new average with respect to given data using the variable $x$ and formula for average.