Question

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

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

Answer: (B)

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