Question

A number is greater than twice the other number by 8. Also, 5 times the smaller number exceeds the greater by 12. Convert these relations into simultaneous equations.

• A. $x-2y-8=0$
  And, $x-5y+12=0$
• B. $x-2y+8=0$
  And, $x-5y-12=0$
• C. $2x-y-8=0$
  And, $5x-y+12=0$
• D. $x-2y-12=0$
  And, $x-5y+8=0$

Answer 1

The correct option is A $x-2y-8=0$

And, $x-5y+12=0$
Let $x$ and $y$ be the two numbers such that $x>y$.
According to the question $x$ is greater than $2y$ by $8$.
$\Rightarrow x=2y+8$
$\Rightarrow x-2y-8=0$
Similarly, other statement says $5y$ is greater than $x$ by $12$.
$\Rightarrow 5y=x+12$
$\Rightarrow 0=x-5y+12$
So, the two equations are
$x-2y-8=0$
And, $x-5y+12=0$