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Arithmetic mean and Harmonic mean of two numbers are in the ratio 2 : 3. What will be the ratio of geometric mean of the numbers to sum of the numbers?

Arithmetic mean and Harmonic mean of two numbers are in the ratio 2 : 3. What will be the ratio of geometric mean of the numbers to sum of the numbers? Correct Answer √(3/8)

Calculation:

Let AM and HM are 2k and 3k respectively,

GM2 = AM × HM

⇒ GM2 = 2k × 3k = 6k2

⇒ GM = k√6

AM = half of the sum of numbers,

∴ Sum of numbers = 4k

Required ratio = (k√6)/(4k)

⇒ √(3/8)

Additional Information

The relation between AM, GM, and HM is AM × HM = GM2

The arithmetic mean of numbers a and b is given by (a + b)/2 or half of the sum of numbers.

The geometric mean of numbers a and b is given by √ab or the square root of the product of numbers.

The harmonic mean of the numbers a and b is given by 2ab/(a + b).

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