Question: A man whose bowling average is 12.4 takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number of wickets taken by him before his last match is:

1. 85
2. 78
3. 72
4. 64
5. 62

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

The problem statement states that:
Given:

• A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4.

Find out:

• The number of wickets taken by him before his last match.

We can solve the problem by using the formula:
Bowling average = Runs / Wicket

Old Average = 12.4
New inning scored in match = 26/5 = 5.2

Let the number of wickets taken by the bowler before his last match = x
New average = (12.4*x + 26) / (x + 5) = 12

This implies, 12x + 60 = 12.4x + 26
That is 0.4x = 34
That is x = 85
Hence, the number of wickets taken by the bowler before his last match = 85.

Approach Solution 2:

The problem statement implies that:
Given:

• A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4.

Find out:

• The number of wickets taken by him before his last match.

Let the number of wickets taken by the bowler before his last match be N.
Therefore, the number of runs given by the bowler before the match = (N−5) × 12.4 + 26
= 12.4N − 62 + 26
= 12.4N − 36
Average of the bowler before the match = 12.4N − 36 / N

As per the question, the average of the bowler before the match =12.4 − 0.4 = 12

Equating both averages, we get
12.4N − 36/N = 12
=> 12.4N−12N = 36
=> N = 36/0.4
=> N = 90

Therefore, the number of wickets taken by the bowler before the last match = N − 5
= 90 − 5
= 85

Hence, the number of wickets taken by the bowler before his last match = 85

Approach Solution 3:

The problem statement informs that:
Given:

• A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4.

Find out:

• The number of wickets taken by him before his last match.

Let's initially say the man has taken “a” wickets with a bowling speed of 12.4 which means he takes one wicket after giving the 12.4 runs.
So the total runs scored would be 12.4a and in this match, he gave 26 runs.
So total runs =12.4a+26 and total wickets become =a+5

Now we know the new bowling average so we can find the value of “a” easily

Here, the bowling average of a man is 12.4. This means he takes one wicket after giving the 12.4 runs and now takes 5 wickets for 26 runs and thereby decreasing his average by 0.4.
This means that his new bowling average becomes 0.4 less than the initial bowling average. Therefore new bowling average =12.4−0.4=12

Let initially the men have taken “a” wickets with a bowling speed of 12.4
So for taking “a” wicket he has given 12.4a runs.
Now his new average is 12 and has taken 5 wickets by giving 26 runs.
Already he has given 12.4a so the total runs given by him=12.4a+26

As we know he had taken “a” wickets in the initial match and now 5
Therefore, the total number of wickets now = a+5

We know that the bowling average is equal to the ratio of the number of total runs and the number of wickets taken.
So, new bowling average= total runs scored/total wickets taken
12 = 12.4a+26/a+5
⇒12(a+5) = 12.4a+26
⇒12a+60 =12.4a+26
⇒34 = 0.4a
⇒a = 34/0.4 = 85
Therefore, the value of a = 85.

Hence, the number of wickets taken by the bowler before his last match = 85

“A man whose bowling average is 12.4 takes 5 wickets for 26 runs”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must hold solid knowledge of mathematics. The candidates can follow GMAT Quant practice papers to practise varieties of questions that will enable them to improve their mathematical understanding.

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