Question

The H.M. between two numbers is $\frac{16}{5}$, their A.M. is A and G.M. is G. If $2A+G^2=26$, then the numbers are

• A. 6,8
• B. 4,8
• C. 2,8
• D. 1,8

Answer 1

Answer: (C)

Let $a$ and $b$ are two numbers
$\frac{2ab}{a+b}=\frac{16}{5}$.........(1)
$\frac{a+b}{2}=A\text{ and }\sqrt{ab}=G$
$\because 2A+G^2=26$
$\Rightarrow (a+b)+ab=26$....(2)
$\Rightarrow \frac{10ab}{16}+ab=26$
$\Rightarrow 26ab=26\times 16$
$\Rightarrow ab=16,a+b=10$
$\therefore$ from (1), we get
So $a,b$are $(2,8)$