Question

The value of $y$ increased by $12$ is directly proportional to the value of $x$ decreased by $6$. If $y=2$ when $x=8$, find the value of $x$ when $y=16$.

• A. $9$
• B. $10$
• C. $16$
• D. $20$
• E. $28$

Answer 1

The correct option is B $10$

As given $y$ is directly proportional to $x$. i.e: $y=kx$ for some constant $k$.
According to question, if the value of $y$ is increased by $12$ is proportional to the value of $x$ decreased by $6$.
i.e: $y+12=k(x-6)$
Plugging $x$ $=8$ and $y$ $=2$
$2+12=k(8-6)$
$14=2k$ ; $k=7$
The new equation is $y+12=7(x-6)$
Plugging $y$ $=16$ in above equation.
$\Rightarrow 16+12$ $=7x-42$
$\Rightarrow 7x=70$

$\Rightarrow x$ $=10$
Hence, option B is correct.