Question

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

Answer 1

Hint: In order to compute the number of wickets taken till the last match, we consider a variable x which is the number of wickets taken till the last match. Then we 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 answer:
Let the number of wickets taken by the cricketer until the last match be ‘x’.
Let the number of runs scored be ‘y’.
∴Hence, his bowling average i.e. $
  \dfrac{{\text{y}}}{{\text{x}}} = 12.4 \\
   \Rightarrow {\text{y = 12}}{\text{.4x}} \\
$
Now, the average is reduced by 0.4, also 5 wickets and 26runs are added
⟹Average = $\dfrac{{{\text{total runs}}}}{{{\text{total wickets}}}} = \dfrac{{{\text{12}}{\text{.4x + 26}}}}{{{\text{x + 5}}}} = 12.4 - 0.4$
⟹12x + 60 = 12.4x + 26
⟹0.4x = 34
⟹x = 85
The number of wickets taken by the cricketer till the last match = 85.
Hence, Option D is the right answer.
Note: In order to solve this type of questions the key is to establish a relation between the given average and the new average, with respect to the given data, using a variable x and formula for average. On solving x we get the answer. These types of questions require a careful observation of what’s given in the question.