Q49 / 90 · KVPY 2013 (SB/SX) · Mathematics

If $a, b$ are positive real numbers such that the lines ax $+9 y=5$ and $4 x+b y=3$ are parallel, then the least possible value of $a+b$ is

A
13
Correct answer
B
12
C
8
D
6

Solution

$\frac{a}{4}=\frac{9}{b} \Rightarrow a b=36$ using $A M \geq G \cdot M$ $\frac{a+b}{2} \geq \sqrt{a b} \Rightarrow a+b \geq 12$

Hence, the correct answer is option: 'B'.

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