A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number.
for the original number:
unit digit --- x
tens digit --- y
the original number is 10y+x
reversed number:
unit digit --- y
tens digit --- x
reversed number is 10x + y
10y+x - (10x+y) = 9
9y - 9x = 9
x - y = 1 , but
x + y = 13
add them:
2x = 14
So x = 7 and y = 6
The original number is 67