Question

A cricketer gives 12.4 runs per wicket. He gives 26 runs and takes 5 wickets in a match after which his average becomes 12 runs per wicket. How many wickets had been taken till the last match?

Answer 1

Hint – In this particular question assume any variable be the number of wickets before the last match so the total number of wickets he takes till the last match is the sum of the variable and the wickets he take in the last match and the average runs per wicket is the ratio of total number of runs to the total number of wickets so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
A cricketer gave 12.4 runs per wicket.
In his last match he gave 26 runs and took 5 wickets.
So that his average becomes 12 runs per wicket.
Now we have to calculate how many wickets had been taken till the last match?
Let he takes X wickets before the last match.
Therefore he takes (X + 5) wickets till the last match
Now as we know that the average runs per wicket is the ratio of total number of runs to the total number of wickets.
So, Average runs per wicket = $\dfrac{{{\text{total number of runs}}}}{{{\text{total number of wickets}}}}$
Now from the first condition i.e. before the last match he gave 12.4 runs per wicket.
Therefore, 12.4 = $\dfrac{{{\text{total number of runs}}}}{{\text{X}}}$...................... (1)
Now after the last match he gave 12 runs per wicket, and give 26 runs and takes 5 wicket
Therefore, 12 = $\dfrac{{{\text{total number of runs}} + 26}}{{X + 5}}$
Therefore, $12\left( {X + 5} \right) - 26 = $total number of runs..................... (2)
Now from equation (2) substitute the value of total number of runs in equation (1) we have,
Therefore, 12.4 = $\dfrac{{12X + 60 - 26}}{X}$
Now simplify this we have,
$ \Rightarrow 12.4X - 12X = 34$
$ \Rightarrow 0.4X = 34$
$ \Rightarrow X = \dfrac{{34}}{{0.4}} = 85$
So the total wickets he takes till the last match = (85 + 5) = 90 wickets.
So this is the required answer.

Note – Whenever we face such types of question the key concept we have to remember is that Average runs per wicket = $\dfrac{{{\text{total number of runs}}}}{{{\text{total number of wickets}}}}$, so according to given two conditions make two equations as above and form any equation substitute the value of total number of runs in another equation as above and evaluate X as above then add the last match wickets in X, we will get the required answer.