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If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation?
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If the combined harmonic mean of 18 observations is 3 and harmonic mea...
**Solution:**
Given,
- Combined harmonic mean of 18 observations = 3
- Harmonic mean of first 10 observations = 27
Let the sum of all 18 observations be S, then
- Combined harmonic mean = 18/S
- Harmonic mean of first 10 observations = 10/x, where x is the sum of first 10 observations.
- Harmonic mean of remaining 8 observations = 8/y, where y is the sum of remaining 8 observations.
**Finding the value of S:**
- Combined harmonic mean = 3
- So, 18/S = 3
- Therefore, S = 18/3 = 6
**Finding the value of x:**
- Harmonic mean of first 10 observations = 27
- So, 10/x = 27
- Therefore, x = 10/27
**Finding the value of y:**
- We know that sum of all 18 observations is S = 6
- Sum of first 10 observations is x = 10/27
- So, the sum of remaining 8 observations = S - x = 6 - 10/27 = 152/27
**Finding the harmonic mean of remaining 8 observations:**
- Harmonic mean of remaining 8 observations = 8/y
- Substituting the value of y in the above equation, we get:
- Harmonic mean of remaining 8 observations = 8/(152/27)
- Simplifying, we get:
- Harmonic mean of remaining 8 observations = 54/19
Therefore, the harmonic mean of remaining 8 observations is 54/19.
Given,
- Combined harmonic mean of 18 observations = 3
- Harmonic mean of first 10 observations = 27
Let the sum of all 18 observations be S, then
- Combined harmonic mean = 18/S
- Harmonic mean of first 10 observations = 10/x, where x is the sum of first 10 observations.
- Harmonic mean of remaining 8 observations = 8/y, where y is the sum of remaining 8 observations.
**Finding the value of S:**
- Combined harmonic mean = 3
- So, 18/S = 3
- Therefore, S = 18/3 = 6
**Finding the value of x:**
- Harmonic mean of first 10 observations = 27
- So, 10/x = 27
- Therefore, x = 10/27
**Finding the value of y:**
- We know that sum of all 18 observations is S = 6
- Sum of first 10 observations is x = 10/27
- So, the sum of remaining 8 observations = S - x = 6 - 10/27 = 152/27
**Finding the harmonic mean of remaining 8 observations:**
- Harmonic mean of remaining 8 observations = 8/y
- Substituting the value of y in the above equation, we get:
- Harmonic mean of remaining 8 observations = 8/(152/27)
- Simplifying, we get:
- Harmonic mean of remaining 8 observations = 54/19
Therefore, the harmonic mean of remaining 8 observations is 54/19.
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If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation?
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If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation?.
If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the combined harmonic mean of 18 observations is 3 and harmonic mean of first 10 observation is 27 find the harmonic mean of remaining eight observation?.
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