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A bowler gives 16.2 runs per wicket. He gives 40 runs and takes 4 wickets in a last match after which his average becomes 15.4 runs per wicket. How many wickets had been taken by him before the last match?
  • a)
    43
  • b)
    32
  • c)
    27
  • d)
    36
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A bowler gives 16.2 runs per wicket. He gives 40 runs and takes 4 wick...
GIVEN:
Bowler’s old average = 16.2
Bowler’s new Average = 15.4
FORMULA USED:
Bowling average = Total runs conceded/Total wicket taken
CALCULATION:
Let the total number of wickets be x
Then, bowling average = 16.2
Runs conceded = 16.2 x
Now, (16.2 x + 40)/(x +  4) = 15.4 
16.2 x + 40 = 15.4 (x + 4)
16.2 x + 40 = 15.4 x + 61.6
0.8 x = 61.6 – 40
x = 21.6/0.8 = 27
Alternate method:
By Allegation:

 
Hence total number of wickets taken before last match = 27
(Note – if question is to find the number of wickets till last match, then answer will be = 27 + 4 = 31)
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Most Upvoted Answer
A bowler gives 16.2 runs per wicket. He gives 40 runs and takes 4 wick...
Given:

- Bowler's previous average = 16.2 runs per wicket
- Bowler gave 40 runs and took 4 wickets in the last match
- Bowler's new average = 15.4 runs per wicket

To find:

- Number of wickets taken by the bowler before the last match

Solution:

Let's assume that the bowler had taken 'x' wickets before the last match.

Before the last match, the total runs given by the bowler = 16.2x

After the last match, the total runs given by the bowler = 16.2x + 40

Before the last match, the average runs given per wicket = 16.2

After the last match, the average runs given per wicket = 15.4

Using the formula for average, we can write:

Before the last match:

16.2x / x = 16.2

x = 16.2

After the last match:

(16.2x + 40) / (x + 4) = 15.4

16.2x + 40 = 15.4x + 61.6

0.8x = 21.6

x = 27

Therefore, the bowler had taken 27 wickets before the last match.

Answer: Option (c) 27
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