Question

the sum of two digit number is 10.when digits are reversed number decreas by 54.find change number

Answer 1

let the digit at ones place by x
and the digit at tens place be y.
then the no. = 10y+x
if the digits are reversed then the new number = 10x-y
A/O x+y = 10  ...................(i)
A/O 10y +x   =  10x+y +54 
       10y-y = 10x-x +54
       9y = 9y+54
       y = x+6   
       x-y  = -6 ................(ii)
adding eq. (I) and (ii)
         2x =4
          x = 2
   in (i)  x+y = 10
            y = 8
the initial number = 82.
the reversed number = 28