Question

GM and HM of two numbers are $10$ and $8$, respectively. The numbers are

• A. $5,20$
• B. $4,25$
• C. $2,50$
• D. $1,100$

Answer 1

The correct option is A

$5,20$

Explanation for the correct option:

Step 1. Let $\mathit{a}\mathbf{,}\mathbf{}\mathit{b}$ be the two numbers:

Given,

$GM=10$

$\Rightarrow$$\sqrt{ab}=10$

$\Rightarrow$ $ab=100$ …(1)

$HM=8$

$\Rightarrow$$\frac{2ab}{(a+b)}=8$

Step 2. Substitute the value of $\mathit{a}\mathit{b}$

$\frac{2\times 100}{(a+b)}=8$

$\Rightarrow$$a+b=\frac{200}{8}$

$\Rightarrow$$a+b=25$ ….(2)

Step 3. By solving equation (1) and (2), we get

$\mathit{a}\mathbf{}\mathbf{=}\mathbf{}\mathbf{20}\mathbf{,}\mathbf{}\mathit{b}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}$

Hence, option(A) is correct.