Question

A number of two digits is such that twice the ten digit it is 6 greater than the unit digit. When the digits are reversed the number is increased by 9. Find the number

Answer 1

10x+y - a two digit number
x - ten digit
y - unit digit

$2x=y+6\\ 10y+x=10x+y+9\\\\ y-2x=-6\\ 9y-9x=9\\\\ y-2x=-6\\ y-x=1\\\\ y-2x=-6\\ -y+x=-1\\ ------\\ -x=-7\\ x=7\\\\ y-7=1\\ y=8\\\\ 10\cdot7+8=\boxed{78}$