Question

The sum of the digits of a two-digit number is 5. On adding 27 to the number it's digits are reversed. Find the original number.

Answer 1

Let the digits be x and y
then the no = 10x + y
given that sum of digits = 2
⇒ x+ y = 5  --------------(1)
On adding 27 we get the reverse of the no
⇒ 10x+y+27 = 10y +x
⇒10x -x +y - 10y +27 = 0
⇒9x - 9y = - 27  --------------(2)
Solving (1) and (2)
       9x - 9y = -27
       x   + y   = 5
 
      9x - 9y = -27
    9[x  +  y  =   5]
  
      9x - 9y = -27
      9x + 9y = 45
    
⇒  18x       = 18
⇒   x = 18/18
∴    x = 1 in eq (1)
⇒ x+y = 2
⇒ 1 +y = 2
⇒ y = 2-1
∴ y = 1
∴ the no = 10x+y = 10(1) + 1 = 10+1 = 11