Q. If geometric mean and harmonic mean between two different numbers are 12 and $\frac{48}{5}$ respectively, then one number is

1406 218 Rajasthan PETRajasthan PET 2009 Report Error

A

4

B

6

C

8

D

10

Solution:

Let two numbers are a and b. Geometric mean
$= ab$
$\Rightarrow$ $12 = ab$
$\Rightarrow$ $ab = 144$ ...(i) and harmonic mean
$= \frac{2 ab}{a + b}$
$\Rightarrow$ $\frac{48}{5} = \frac{2 ab}{a + b}$
[From Eqs. (i)] $\Rightarrow$ $(a + b) = 30$ ...(ii)
On solving Eqs. (i) and (ii), we get $a = 6, b = 24$