The sum of the digits of a two-digit number is 12. If the digits are reversed, seven times the new number equals to four times the original number. Find the number.

The sum of the digits of a two-digit number is 12.

If the digits are reversed, seven times the new number equals four times the original number.

Let the two-digit number be$10x+y$, where:

$x$is the tens digit

$y$is the units digit 

Now, 

From the second condition (seven times the reversed number equals four times the original number):

Substitute $x=2y$ into the first equation:

Thus,  The number is 84.