Question

the sum of two digits of a two digit number is 15 and if 9 is added to the number the digits are interchanged.find the number

Answer 1

let the number 10×x+y
sum of its two digit x+y=15
x=15-y ----------1eqn
and if 9 is added to the original digit the number gets enter changed
9+10x+y=10y+x
9+9x-9y=0
9(1+x-y)=0
1+x=y
putting value from eqn 1
we have
1+15-y=y
2y=16
y=8

hope it will help you