Sequence And Series Question 369
Question: If the A.M. of two numbers is greater than G.M. of the numbers by 2 and the ratio of the numbers is $ 4:1 $ , then the numbers are
[RPET 1988]
Options:
A) 4, 1
B) 12, 3
C) 16, 4
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Suppose that required numbers are $ a $ and $ b $ . Now A.M. $ =\frac{a+b}{2} $ and G.M. $ =\sqrt{ab} $ Under conditions, A.M.=G.M.+ 2
$ \Rightarrow $ $ \frac{a+b}{2}=\sqrt{ab}+2 $ ……(i) and $ \frac{a}{b}=\frac{4}{1} $
$ \Rightarrow $ $ a=4b $ …..(ii) From (ii) and (i), we get $ a=16 $ and $ b=4 $ .
BETA
