Question

The A.M. between two positive numbers exceeds the GM by 5 and the GM exceeds the H.M. by 4 . Then the numbers are-

• A. 10,40
• B. 10,20
• C. 20,40
• D. 10,50

Answer 1

Answer: (A)

Let the two positive numbers are $a$ and $b$
By given condition
$\text{ A.M. }=\text{ GM. }+5\text{ or }A=G+5$..........(i)
$\text{ G.M. }=\text{ HM. }+4\text{ or }G=H+4$.......(ii)
we know $G^2=AH$
or $G^2=(G+5)(G-4)$ [By (i) and (ii)]
$\Rightarrow G=20$
$\therefore A=25$ and $H=16$
Again $A=\frac{a+b}{2}$
$\therefore \frac{a+b}{2}=25$
$\Rightarrow a+b=50$
$G=\sqrt{ab}$
$\therefore \sqrt{ab}=20$
$\Rightarrow ab=400$
solving the equation we get $a=10,b=40$