Question

The difference between two numbers is $8$. If $12$ is added to the bigger number the result will be three times the smaller number. Find the numbers.

Answer 1

Let the two numbers be $x$ and $y$, where $x$ being the greater one.

Then according to the question,

$x-y=8$ ....(1) and $x+12=3y$ ..(2)

From ..(2),

$x=3y-12$

Putting this in the ...(1)

$3y-12-y=8$

$2y=12+8=20$

$\therefore y=10$

From ...(1)

$x-10=8$

$x=8+10$

$\therefore x=18$

Therefore, the numbers are $18$ and $10$