Question

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

• A. $13$
• B. $12$
• C. $8$
• D. $6$

Answer 1

Answer: (B)

$12$

Two lines are parallel when their slopes are equal.

Since a,b are positive real numbers, $\frac{a}{4}=\frac{9}{b}$

$\Rightarrow ab=36$

Since $36$ is the square of $6,a+b$ would be minimum when $a$ and $b$ are equal and in this case, $6$ each.

Thus, $a+b$ has the minimum value of $6+6=12$