Question

The sum of two numbers is $8$. If their sum is $4$ times their difference. Find the numbers.

• A. $4,4$
• B. $6,2$
• C. $5,3$
• D. None of these

Answer 1

The correct option is C $5,3$

Let the first number be $x$ and second number $y.$

According to question
$x+y=8\dots \left(i\right)$

$4(x-y)=8$

$\Rightarrow x-y=2\dots \left(ii\right)$

Add equations $\left(i\right)$ and $\left(ii\right),$
$\begin{array}{cc}\left(x+y\right)+\left(x-y\right)& =8+2\\ 2x& =10\\ x& =5\end{array}$

Substitute $x=5$ in $\left(i\right),$
$\begin{array}{cc}\left(5\right)+y& =8\\ y& =8-5\\ y& =3\end{array}$

So, the numbers are $5$ and $3.$