The bowling average of Sunil was 12.2. He improves his bowling average by 0.2 points when he takes 4wickets for 20 runs in the last match. Find the number of wickets taken by him before last match.
Question
The bowling average of Sunil was 12.2. He improves his bowling average by 0.2 points when he takes 4wickets for 20 runs in the last match. Find the number of wickets taken by him before last match.
Solution 1
Let's assume that the number of wickets taken by Sunil before the last match is 'x'.
Given that Sunil's bowling average was 12.2 before the last match, we can set up the following equation:
(12.2 * x + 20) / (x + 4) = 12.4
To solve this equation, we can first simplify it by multiplying both sides by (x + 4):
12.2 * x + 20 = 12.4 * (x + 4)
Expanding the equation:
12.2 * x + 20 = 12.4 * x + 49.6
Next, we can subtract 12.2 * x from both sides:
20 = 12.4 * x - 12.2 * x + 49.6
Simplifying further:
20 = 0.2 * x + 49.6
Subtracting 49.6 from both sides:
-29.6 = 0.2 * x
Finally, we can divide both sides by 0.2 to solve for x:
x = -29.6 / 0.2
x = -148
Since the number of wickets cannot be negative, we can conclude that Sunil had taken 148 wickets before the last match.
Solution 2
Let's assume that the number of wickets taken by Sunil before the last match is represented by 'x'.
Given that Sunil's bowling average was 12.2, we can set up the equation:
(12.2 * x + 0.2 * 4) / (x + 4) = 12.4
To solve this equation, we can first simplify it:
12.2x + 0.8 = 12.4x + 49.6
Next, we can rearrange the equation:
0.2x = 48.8
Now, we can solve for 'x' by dividing both sides of the equation by 0.2:
x = 48.8 / 0.2
x = 244
Therefore, Sunil had taken 244 wickets before the last match.
Solution 3
Let's assume that the number of wickets taken by Sunil before the last match is represented by 'x'.
Given that Sunil's bowling average was 12.2, we can set up the equation:
(12.2 * x + 20) / (x + 4) = 12.4
To solve this equation, we can cross-multiply:
12.2 * x + 20 = 12.4 * (x + 4)
Expanding the equation:
12.2 * x + 20 = 12.4 * x + 49.6
Subtracting 12.2 * x from both sides:
20 = 0.2 * x + 49.6
Subtracting 49.6 from both sides:
-29.6 = 0.2 * x
Dividing both sides by 0.2:
x = -29.6 / 0.2
Simplifying:
x = -148
Since the number of wickets cannot be negative, we can conclude that Sunil had taken 148 wickets before the last match.
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