Question

A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets, taken by him, before his last match is ______
A. 85
B. 78
C. 72
D. 64

Answer 1

Hint: We will assume that the number of wickets taken in the last match be $x$. Then, the number of total wickets taken is $x+5$ and the total number of runs scored till the last match will be $12.4x+26$. We will take the average and equate it to 0.4 less than 12.4. Solve the equation to find the value of $x$.

Complete step-by-step answer:
We are given that the bowling average is 12.4
Let the bowler has taken $x$ wickets before his last match, then the number of runs given by him are $12.4x$
We are given that the bowler has given 26 runs in the last match.
Therefore, the number of total runs given by the bowler are $12.4x+26$
And the wickets taken in the last match are 5.
Then, the total number of wickets taken by the bowler in all the matches are $x+5$
We know that the average is calculated by dividing the total number of runs given by the total number of wickets taken by the bowler.
Hence, the average of the bowler is ${\displaystyle \frac{\text{total number of runs given}}{\text{Number of wickets taken}}}={\displaystyle \frac{12.4x+26}{x+5}}$
We are also given that the total average is decreased by 0.4
Then, the average of the bowler is $12.4-0.4=12$
Hence, ${\displaystyle \frac{12.4x+26}{x+5}}=12$
Cross-multiply and form an equation in $x$.
$$\begin{gathered} 12.4x+26=12x+60 \\ \Rightarrow 0.4x=34 \end{gathered}$$
Divide both sides by 0.4
$x=85$
Therefore, the number of wickets taken by the bowler in the last match is 85
Hence, option A is correct.

Note: Bowling average is calculated as ${\displaystyle \frac{\text{total number of runs given}}{\text{Number of wickets taken}}}$. Also, the equation should be formed according to the given condition.