Find the possible original number(s).

Question

The ones digit of a two-digit number if four more than the tens digit. If the ones digit and the tens digit are interchanged, the value of the new number is 36 more than the original number. Find the possible original number(s).

Answer 1

The 2nd condition just gives the answer:

 

   36   63

   

     let's take a 2digit number - ab  a, b are digits

 

        N -   value of ab = b + 10a

        M -   value of interchange= 10 b + a

 

       M - N = 10b + a - b - 10a = 9a - 9b

 

           if a = b+4

 

            then

 

         M- N = 9 ( b +4 ) - 9b = 36

 

          Always 2 digit number, if ones digit is 4 more than the tens digit, then difference between

         interchange of digit and the original number is 36

 

         Examples:

 

           15     51        51 -15 =36

 

           26     62        62 - 26 = 36

 

           37    73         73 - 37 = 36

 

           48   84          84 - 48 = 36

 

          59     95         95 - 59 = 36