Question

Form the pair of linear equations for the following problem and find their solution by substitution method.

The difference between the two numbers is $26$ and one number is three times the other.

• A. $x-y=26$ and $x=3y$, $x=33$ and $,y=11$
• B. $x-y=26$ and $x=3y$, $x=39$ and $y=13$
• C. $x-y=13$ and $x=3y$, $x=75$ and $y=25$
• D. None of these

Answer 1

Answer: (B)

$x-y=26$ and $x=3y$, $x=39$ and $y=13$

Let the two numbers be $x$ and $y(x>y)$.

In question given that the difference between two number is $26$.
$\Rightarrow x-y=26$ .......(i)

And the one number is $3$ times of the other number
$\Rightarrow x=3y$ .......(ii)

Now putting $x=3y$ in equation (1)
$\Rightarrow 3y-y=26$
$\Rightarrow 2y=26$
$\Rightarrow y=13$

Now substituting $y$ value in (2),
$\Rightarrow x=3\times 13$
$\Rightarrow x=39$

Hence, $x=39$ , $y=13$