Question

The A.M. of two numbers is $34$ and their G.M. is $16$. The two numbers are

• A. $60,8$
• B. $64,4$
• C. $56,12$
• D. $52,16$

Answer 1

Answer: (B)

$64,4$

Let the numbers are $a$ and $b$
A.M between a and b is $34$
$\therefore \frac{a+b}{2}=34$
$a+b=68$........ (1)
G.M between a and b is 16
$\therefore \sqrt{ab}=16$
$\therefore ab=256$
We know, $(a-b{)}^2=(a+b{)}^2-4ab$
$(a-b{)}^2=(68{)}^2-4\times 256$
$(a-b{)}^2=4624-1024$
$(a-b{)}^2=3600$
$a-b=\sqrt{3600}=60$.......(2)
Adding 1 and 2,
$2a=128$
$a=64$
from $a+b=68$
$b=68-a\to 68-64=4$
The numbers are $64,4$.