Sequence And Series Question 472
Question: The harmonic mean H of two numbers is 4 and the arithmetic mean A and geometric mean G satisfy the equation $ 2A+G^{2}=27 $ . The two numbers are
Options:
A) 6, 3
B) 9, 5
C) 12, 7
D) 3, 2
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let two numbers be a and b. Given $ \frac{2ab}{a+b}=4\Rightarrow ab=2( a+b ) $ $ 2A+G^{2}=27 $
$ \Rightarrow 2( \frac{a+b}{2} )+ab=27 $
$ \Rightarrow ab=18 $ and $ a+b=9\Rightarrow a+b=9 $ On solving these we get $ a=3 $ & $ b=6 $ or $ a=6 $ & $ b=3. $
BETA
