Question

A two digit no such that the sum of the digit is 12.when 1 is added to the no the digits interchange their places.find the nos.

Answer 1

There is a mistake in the given problem... It should be that, when 18 is added, the digits interchange their positions.  If 1 is added then, the digits do not interchange places.

two digit number  A B.
  sum of the two digits = A + B = 12    --- (1)
  The value of the number =  10 * A + B

Now 18 is added to the number:    the value becomes :  10 A + B + 18
 The number becomes:  B A    whose value = 10 B + A

   Hence,  10 B + A = 10 A + B + 18
               9 B = 9 A + 1
                9 B = 9 (12 - B) + 1        -- by (1)
               18 B = 108 + 18
     B = 7
     A = 5

Given number is  57    ,    you add 18  ,  it becomes    75.

Answer 2

Given number is 57 , by adding 18 We get 75......