Question

The sum of the digits of a two digit number is 9.if 27 is added to it , the digits of the number gets reversed . find the number?

Answer 1

Let the digits be x and y... and so, the original number be 10x + y ( since x in tenth place and y in unit place)

so, given : sum of the digits = x + y = 9 ---------> (A)
                  
reversing the digits means y in tenth place and x in unit place.. so, the reversed number be 10y + x
         
   given: orig num + 27 = reversed number
 
          so, 10x + y + 27 = (10y + x) 
           simplifying :   9x - 9y = -27       ------------> (B)

solving 2 eqns (A) & (B) ,
 we get x = 3 and y = 6

so the original number is 10x + y = 10(3) + 6 = 36
   & the reversed number is 10y + x = 10(6) + 3 = 63
    & the reversed number 63 is 27 + (original number) 36

Ans: the original number is 36

Answer 2

Here is your solution

Given :-

The sum of the digits of a two digit number is 9.
if 27 is added to it , the digits of the number gets reversed .

Now

Let ,

x and y are the two digits of a two-digit number.

The two-digit number = 10x + y

reversed number = 10y + x


x + y = 9 ------------1

A/q

10x + y + 27 = 10y + x
9y - 9x = 27
y - x = 3 -----------2

Substract equation 2 from equation 1

2x = 6

x = 3✔


y = 9 - x
y= 9 - 3
y= 6✔


The two digit number = 10x + y = (10 × 3) + 6 = 36.

Hope it helps you