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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Sequences and Series

NDA 2010 · Mathematics · Sequences and Series

If the AM and HM of two numbers are 27 and 12 respectively, then...

If the AM and HM of two numbers are 27 and 12 respectively, then what is their GM equal to?

Options

  1. A12
  2. B18
  3. C24
  4. D27

Correct answer

A. 12

Step-by-step solution

Let the two numbers be aandba and b. So, a+b2=27\frac{a+b}{2}=27, and 1a+1b2=12⇒b+a2ab=12⇒ab=2712=94∴ G.M. =ab=32\begin{aligned} & \frac{\frac{1}{a}+\frac{1}{b}}{2}=12 \Rightarrow \frac{b+a}{2 a b}=12 \\ & \Rightarrow a b=\frac{27}{12}=\frac{9}{4} \\ & \therefore \text{ G.M. }=\sqrt{a b}=\frac{3}{2} \end{aligned}
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