Question
Download Solution PDFThe harmonic mean and the geometric mean of two numbers are 10 and 12 respectively. What is their arithmetic mean?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
The harmonic mean and the geometric mean of two numbers are 10 and 12 respectively
Concept used :
(Geometric mean)2 = Harmonic mean × Arithmetic mean
Calculations :
according to the formula given above
(12)2 = 10 × Arithmetic mean
⇒ Arithmetic mean = 144/10
⇒ 14.4
∴ Option 4 will be the correct answer.
Alternate Method
Concept:
A.M. between a and b =
G.M. between a and b =
H.M. between a and b =
Calculation:
Given, G.M. = 12, H.M. = 10
ab = 144 ........(1)
2ab = 10a + 10b
ab = 5 (a + b)........(2)
From equation (1) and (2)
144 = 5 (a + b)
But, we know that,
A.M. between a and b =
Therefore, AM = 14.4
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