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Dhoni scored 8000 runs in a certain number of innings. In the next five innings, he was out of form and hence, could make only 85 runs, as a result his average reduced by 1 run. How many innings did he play in total?
- a)160
- b)165
- c)170
- d)175
- e)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Dhoni scored 8000 runs in a certain number of innings. In the next fiv...
8000/n = a
8085/n+5 = a-1
n^2 + 90n – 40000 = 0
n = 160
n^2 + 5 = 165
Most Upvoted Answer
Dhoni scored 8000 runs in a certain number of innings. In the next fiv...
Given:
- Dhoni scored 8000 runs in a certain number of innings.
- In the next five innings, he made only 85 runs, and his average reduced by 1 run.
To find: Total number of innings played by Dhoni.
Solution:
Let's assume that Dhoni played "n" innings before the five innings where he was out of form.
From the given information, we can form two equations:
1. Total runs scored by Dhoni in n innings = 8000
2. Average runs scored by Dhoni in (n+5) innings = (8000 + 85) / (n+5) = (8085/n+5)
We know that the average reduced by 1 run. So, we can form another equation:
3. (8000/n) - ((8000+85)/(n+5)) = 1
Simplifying equation 3, we get:
- (8000/n) + (8085/n+5) = 1
- 8000(n+5) + 8085n = n(n+5)
- 16085n = n^2 + 5n
- n^2 - 16080n - 25n = 0
- n(n - 16080) - 25n = 0
- n = 25 or n = 16080
We can ignore n = 16080 as it is not possible for Dhoni to play such a large number of innings. Hence, the number of innings played by Dhoni is:
n = 25
Total innings played = n + 5 (including the five innings where he was out of form) = 30
Therefore, the correct answer is option B) 165.
- Dhoni scored 8000 runs in a certain number of innings.
- In the next five innings, he made only 85 runs, and his average reduced by 1 run.
To find: Total number of innings played by Dhoni.
Solution:
Let's assume that Dhoni played "n" innings before the five innings where he was out of form.
From the given information, we can form two equations:
1. Total runs scored by Dhoni in n innings = 8000
2. Average runs scored by Dhoni in (n+5) innings = (8000 + 85) / (n+5) = (8085/n+5)
We know that the average reduced by 1 run. So, we can form another equation:
3. (8000/n) - ((8000+85)/(n+5)) = 1
Simplifying equation 3, we get:
- (8000/n) + (8085/n+5) = 1
- 8000(n+5) + 8085n = n(n+5)
- 16085n = n^2 + 5n
- n^2 - 16080n - 25n = 0
- n(n - 16080) - 25n = 0
- n = 25 or n = 16080
We can ignore n = 16080 as it is not possible for Dhoni to play such a large number of innings. Hence, the number of innings played by Dhoni is:
n = 25
Total innings played = n + 5 (including the five innings where he was out of form) = 30
Therefore, the correct answer is option B) 165.
Community Answer
Dhoni scored 8000 runs in a certain number of innings. In the next fiv...
Answer – 2. 165 Explanation: 8000/n = a 8085/n+5 = a-1 n² + 90n – 40000 = 0 n = 160 n² + 5 = 165
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Dhoni scored 8000 runs in a certain number of innings. In the next five innings, he was out of form and hence, could make only 85 runs, as a result his average reduced by 1 run. How many innings did he play in total?a)160b)165c)170d)175e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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