Question

Sum of two numbers is 99 and two digits of a number is interchanged, difference between two numbers is 9

Answer 1

Let the ten's digit be x
& the one's digit be y

according to assumption.....
original no. wii be 10x+y
interchanged no. 10y+x....

according to your question

10x+y+10y+x=99
11x+11y=99
x+y=9.........................(i)

second case

10x+y-(10y+x)=9
10x+y-10y-x=9
9x-9y=9
x-y=1...........................(ii)

adding i & ii

x+y+x-y=9+1
2x=10
x=5

putting in equation ii

x-y=1
5-y=1
y=4

the required no. is
10x+y
10×5+4
50+4
54............
..... Hope this helps you.........
(hope answer is correct)☺