Question

a number constitutes of 2 digits whose sum is 8. if 18 is added to it it's digit will get interchanged. find the number

Answer 1

let the two digits are x and y such that the number is 10x+y
given that x+y=8---------1
also 10x+y+18=10y+x
10x-10y+y-x+18=0
10 (x-y)-(x-y)+18=0
(x-y)(10-1)= -18
(x-y)×9= -18
x-y= -2---------2

equation 1 +equation 2 gives
2x=6=>x=3
put the value of x in equation 1
x+y=8
y=8-3=5
so the number is 35