Posted by emma on Monday, November 21, 2011 at 7:06pm.
n m = 10 n + m
n+m = 8
m n = n + 10 m
n + 10 m - (10 n + m) = 54
-9 n + 9 m = 54
-n + m = 6
but
+n + m = 8
---------- add
0 +2m = 14
m = 7
n = 1
so
17
original:
unit digit -- x
tens digit -- 8-x
the number: 10(8-x) + x
the number reversed: 10x + (8-x)
10x + 8-x - (10(8-x) + x) = 54
10x + 8 -x - 80 + 10x - x = 54
18x = 126
x = 7
unit digit = 7
tens digit = 1
original number 17
number reversed 71
or
original number is 71
number reversed is 17
in both cases the difference between them is 54
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