Question

If the number obtained by interchanging the digits of a 2-digit number is 36 more than that the original number and the sum of the digits is 8,then what is the original number?

Answer 1

let the original number be 10a+b
interchanged number: 10b+a
a+b = 8
according to problem, 

10b+a = 36+10a+b
9b-36-9a=0 
9(b-4-a)= 0
b-4-a=0
b=a+4

substituting b = a+4 in a+b = 8,
a+a+4 = 8
2a=4
a=2

original number= 20+4
                         = 24