Question

The sum of two numbers is 8. If their sum is four times their difference, the numbers are .

• A. 5 and 3
• B. 4 and 4
• C. 1 and 7

Answer 1

The correct option is A 5 and 3

Let the numbers be $x$ and $y$

$\Rightarrow x+y=8$ .....(1) and

$x+y=4(x-y)$ (Assuming x > y)

$\Rightarrow 3x-5y=0$ ......(2)

On multiplying equation (1) by 5, we get

$5x+5y=40$ ......(3)

On adding equations (2) and (3), we get

$8x=40$

$\Rightarrow x=5$

On substituting $x=5$ in equation (1), we get

$5+y=8$

$\Rightarrow y=3$

Therefore, the numbers are 5 and 3.