The A.M of two positive numbers is 15 and their G.M is 12. What is the smaller number?

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Solution

The correct option is C 6
Let a,b be the two numbers then
$A . M = \frac{a + b}{2} = 15$
$\Rightarrow a + b = 30$
and $G . M = \sqrt{a b} = 12$
$\Rightarrow a b = 144$
Now go through options
let a = 6, then b = 24
$a . b = 6 \times 24$
Hence choice (c) is correct.

Alternatively: $(a - b)^{2} = (a + b)^{2} - 4 a b$
$= (30)^{2} - 4 \times 144$
$= 900 - 576 = 324$
$\Rightarrow a - b = \pm 18$
$∴ (a, b) = (6, 24) o r (24, 6)$

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The A.M of two positive numbers is 15 and their G.M is 12. What is the smaller number?

The correct option is C 6Let a,b be the two numbers then A.M=a+b2=15 ⇒a+b=30 and G.M=√ab=12 ⇒ab=144 Now go through options let a = 6, then b = 24 a.b=6×24 Hence choice (c) is correct. Alternatively: (a−b)2=(a+b)2−4ab =(30)2−4×144 =900−576=324 ⇒a−b=±18 ∴(a,b)=(6,24) or (24,6)