Question 133852
10s digit: x
1s digit: y


The original number:  {{{n[o]=10x+y}}}, because a number like 24 could be represented as {{{2*10+4}}}


Reversing the digits makes a new number: {{{n[n]=10y+x}}}


Twice the original number is {{{2(10x+y)}}} and 4 less than that is {{{2(10x+y)-4}}} which we know to be equal to the new number, so:


{{{10y+x=2(10x+y)-4}}}


Simplify:
{{{10y+x=20x+2y-4}}}
{{{10y-2y+x-20x=-4}}}
{{{8y-19x=-4}}}



Since we know that the sum of the digits is 13, we can say {{{x+y=13}}}, or in other words, {{{y=13-x}}}


Substitute:
{{{8(13-x)-19x=-4}}}
{{{104-8x-19x=-4}}}
{{{-27x=-108}}}
{{{x=4}}}


So the 10s digit of the original number (and the ones digit of the new number) is 4.  Therefore the ones digit of the original number must be {{{13-4=9}}}, and the original number must be 49.


Check:
Number is: 49
{{{4+9=13}}}

{{{2*49-4=98-4=94}}} which is the original number with the digits reversed.