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The average of some natural numbers is 15. If 30 is added to the first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural numbers is:
- a)20
- b)30
- c)15
- d)10
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The average of some natural numbers is 15. If 30 is added to the firs...
Problem Analysis:
Let's assume that there are 'n' natural numbers in the given set.
Given:
Average of the natural numbers = 15
Average after adding 30 to the first number and subtracting 5 from the last number = 17.5
Step-by-Step Solution:
Let's solve this problem step by step:
1. Average of the natural numbers = 15
- Sum of the natural numbers = Average * Number of terms
- Sum of the natural numbers = 15 * n
2. Average after adding 30 to the first number and subtracting 5 from the last number = 17.5
- Sum after modifications = Average * Number of terms
- Sum after modifications = 17.5 * n
3. We can calculate the sum after modifications as follows:
- Sum after modifications = (Sum of the natural numbers) + 30 - 5
- Sum after modifications = 15n + 30 - 5
- Sum after modifications = 15n + 25
4. Equating the two sums after modifications:
- 17.5n = 15n + 25
- 17.5n - 15n = 25
- 2.5n = 25
- n = 25/2.5
- n = 10
Therefore, the number of natural numbers in the given set is 10.
Conclusion:
The number of natural numbers in the given set is 10.
Let's assume that there are 'n' natural numbers in the given set.
Given:
Average of the natural numbers = 15
Average after adding 30 to the first number and subtracting 5 from the last number = 17.5
Step-by-Step Solution:
Let's solve this problem step by step:
1. Average of the natural numbers = 15
- Sum of the natural numbers = Average * Number of terms
- Sum of the natural numbers = 15 * n
2. Average after adding 30 to the first number and subtracting 5 from the last number = 17.5
- Sum after modifications = Average * Number of terms
- Sum after modifications = 17.5 * n
3. We can calculate the sum after modifications as follows:
- Sum after modifications = (Sum of the natural numbers) + 30 - 5
- Sum after modifications = 15n + 30 - 5
- Sum after modifications = 15n + 25
4. Equating the two sums after modifications:
- 17.5n = 15n + 25
- 17.5n - 15n = 25
- 2.5n = 25
- n = 25/2.5
- n = 10
Therefore, the number of natural numbers in the given set is 10.
Conclusion:
The number of natural numbers in the given set is 10.
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Community Answer
The average of some natural numbers is 15. If 30 is added to the firs...
According to the question, The average of some natural numbers is 15. If 30 is added to the first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural numbers is
Let the number of natural numbers be x
⇒ 15×x + 30 − 5 = 17.5×x
⇒ 15x + 25 = 17.5x
⇒ 2.5x = 25
⇒ x = 10
Hence, the correct option is (D).
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The average of some natural numbers is 15. If 30 is added to the first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural numbers is:a)20b)30c)15d)10Correct answer is option 'D'. Can you explain this answer?
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