Question

The sum of the digits of a two digit number is 13. The number obtained by interchanging the digits exceeds the given number by 9. Find the number

Answer 1

let x be the tens place digit and y be the unit place digit of a two digit number.
original number=10x+y
from first condition
x+y=13 ---1
from second condition
10y+x=10x+y+9
x-10x+10y-y=9
-9x+9y=9
dividing by 9
-x+y=1 --2
adding equation 1 and 2
x+y =13
-x+y=1
2y=14
y=14÷2
y=7
putting y=7 in equation 1
x+y=13
x+7=13
x=13-7
x=6
original number=10x+y=10×6+7
=60+7=67