Question

The arithmetic mean of two numbers is 10 and their geometric mean is 8. Find the numbers.

• A. 20 and 1
• B. 16 and 4
• C. 10 and 10
• D. 9 and 11

Answer 1

The correct option is B

16 and 4

Let the numbers be a, b.

So, arithmetic mean = $\frac{a+b}{2}$

$⟹$ $\frac{a+b}{2}$ = 10

$⟹$ a+b = 20.

Geometric mean = $\sqrt{ab}$

$⟹$ $\sqrt{ab}$ = 8

$⟹$ ab = 64.

Since a+b = 20 $⟹$ b = 20-a

$⟹$ a $\times$ (20-a) = 64

$⟹$ $a^2$-20a+64 = 0

$⟹$ $a^2$-16a-4a+64 = 0

$⟹$ (a-16) $\times$ (a-4) =0

$⟹$ a= 16 or a= 4.

So, the numbers are 16, 4.