<PRE><B>Question 897351</B>
let a = the 10&#39;s digit
Let b = the units:
:
The difference between a two-digit number and the number obtained by interchanging its digits is 54.
10a+b -(10b+a) = 54
10a + b - 10b - a = 54
9a - 9b = 54
simplify, divide by 9
a - b = 6 
:
If the ratio of the digit at unit&#39;s place to the digits at ten &#39;s place is 1:3;
{{{b/a}}} = {{{1/3}}}
cross multiply
a = 3b
In the 1st simplified equation, replace a with 3b
3b - b = 6
2b = 6
b = 3
find a 
a = 3(3)
a = 9
:
93 is the number
:
what is the difference between the sum and the difference of the digits?
(a+b) - (a-b)
(9+3) - (9-3)
12 - 6 = 6
:
</PRE>