Question

. If the arithmetic mean between two
numbers is 64 and the geometric mean
between them is 16, the harmonic mean
between them is
a) 64 b) 4 c) 16 d) 40
​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Arithmetic mean=64}$

$\textsf{Geometric mean=16}$

$\underline{\textbf{To find:}}$

$\textsf{Harmonic mean}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Relation between A.M, G.M and H.M:}}$

$\boxed{\mathsf{(G.M)^2=A.M{\times}H.M}}$

$\implies\mathsf{(16)^2=64{\times}H.M}$

$\implies\mathsf{256=64{\times}H.M}$

$\implies\mathsf{H.M=\dfrac{256}{64}}$

$\implies\boxed{\mathsf{H.M=4}}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(b)\;is\;correct}$

$\underline{\textbf{Find more:}}$

Answer 2

Given:

Arithmetic mean = 64

Geometric mean = 16

To find:

Harmonic mean =?

Stepwise solution:

• The different types of mathematical and statistical tools are used for calculating the average of given numbers.
• The harmonic mean of two numbers is calculated from the given relation between arithmetic mean, geometric mean, and harmonic mean.

      ⇒ GM² = AM x HM

• On rearranging terms we get:

      ⇒HM = $\frac{GM^{2} }{AM}$

       where, HM = Harmonic mean

       GM= Geometric mean

       AM= Arithmetic mean

      ⇒HM = $\frac{16^{2} }{64}$

      ⇒HM= $\frac{256}{64}$

      ⇒HM = 4

Hence, the correct answer for the harmonic mean is 4 (option b).