Question

Sum of a 2 digit no is 8 and 18 is added to the no. the digit are interchanged

Answer 1

so our number is xy, which means 10x+y.

Anyway, the first sentence say the sum of the 2 digits is 8, so x+y = 8

if we add 18 to the number, ie 10x+y+18 the result is then yx (ie 10y+x)
--> 10x+y+18 = 10y+x
--> 9x + y + 18 = 10y
--> 9x - 9y + 18 = 0
--> 9x - 9y = -18
--> x - y = -2

So we have 2 equations:
x+y=8
x-y=-2
Adding these equations
gives
2X =6
X=6/2 =3
So
Y=8-3 =5

we had number is 35
and in adding 18 we get 53.
Number reversed.