Question

The sum of a two digit number and the number obtained by interchanging the digits is 110. the digits differ by 6. find the numbers.

Answer 1

Hi there !

Let the no: is ten's place  be "x and the no: in unit's place be"y"
Then the original no: is 10x + y

When the digits are interchanged , the no: would be :-
10y + x

given :-

10x + y + 10y+x = 110

11x + 11y = 110

11(x + y) = 110

x + y = 110/11

x + y = 10                -----> [1]

------------------------------
Given :-

x - y = 6            ----> [2]

adding 1 and 2 , we get :-

   x + y = 10
  x - y = 6
=============
 2x = 16

x = 8

x - y = 6

8 -y = 6

y = 2

-----------------------------------------------

The original no: is 10x + y :-
10(8) + 2 = 82

Original no: is 82

No: formed after reversing the digits = 10y + x = 28

Answer 2

The sum of a 2 digit number and the number obtained by reversing the order of its digit is 121, and 2 digit differ by 3. What is the number?

Let the unit digit is ‘x’ and the 10th digit is ‘y’

The number is 10 y +x

Reversed number is 10 x+y

Given 11 x+11 y =121`

x+y=11 [dividing by 11]…….1

Also x-y=3 ……2

solving 1 and 2 we get

x=7 and y=4

The number is 47 [check 47+74=121, 7–4=3]