Question

the sum of the digits of a two digit number is 6 the number obtained by interchanging its digits is 18 more than the original number find the number

Answer 1

Let the unit digit be x and tens digit be y.

x + y=6                 Eq1

Number = 10y+x

Number after reversing the digits = 10x+y

Given,

10x+y-(10y+x)=18

10x+y-10y-x=18

9x-9y=18 = 9(x-y)=18

x-y=2              Eq2

Adding Eq1 and Eq2

x+y+x-y=6+2

2x=8

x=4

x+y=6

y=2

Number = 10y+x = 24