Question

Ratio between two numbers is 1:4 then their am and gm ratio will be

Answer 1

Answer:

Their A.M and G.M ratio will be 5 : 4

Step-by-step explanation:

$\text{Let the two numbers be a and b}$

$\text{Given:}$

$\text{Ratio of the two numbers is 1:4}$

$\text{Then, a=k and b= 4k}$

$\displaystyle\,A.M=\frac{a+b}{2}=\frac{k+4k}{2}=\frac{5k}{2}$

$\displaystyle\,G.M=\sqrt{ab}=\sqrt{k*4k}=\sqrt{4k^2}=2k$

$\text{Now}$

$\displaystyle\frac{A.M}{G.M}=\frac{\frac{5k}{2}}{2k}$

$\displaystyle\frac{A.M}{G.M}=\frac{5}{2*2}$

$\dispalaystyle\frac{A.M}{G.M}=\frac{5}{4}$

$\therefore\textbf{A.M : G.M = 5 : 4}$

Answer 2

Answer:

AM /GM = 5/4

Step-by-step explanation:

Let the two numbers be X and Y .

Given that the ratio between them is 1:4 .

Then, X=k and Y= 4k.

So, Arithmetic Mean (AM)=

$\frac{x + y}{2} = \frac{k + 4k}{2} = \frac{5k}{2}$

And

Geometric Mean (GM) =

$\sqrt{x \times y} = \sqrt{k \times 4k } = \sqrt{4 {k}^{2} } = 2k$

Now, AM /GM =

$\frac{ \frac{5k}{2} }{2k} = \frac{5k}{4k} = \frac{5}{4}$