Question

The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?
Form a pair of linear equations for each of the following problems and find their solution.

Answer 1

Hi ,

Let the two digit number be xy

i.e 10x + y

The number obtained by reversing

the digits = yx

i.e 10y + x

Given sum of two digit number ( xy )

and the number obtained by reversing

the digits ( yx ) is 66.

10x + y + 10y + x = 66

=> 11x + 11y = 66

=> x + y = 6 ---( 1 )

Also given the difference of the digits

is 2 .

| x - y | = 2

x - y = 2 or y - x = 2 ----( 2 )

solving x + y = 6 and x - y = 2 we get,

x = 4 and y = 2 ;

solving x + y = 6 and y - x = 2 we get

x = 2 and y = 4

Therefore ,

The possible two digits is 42 or 24

I hope this helps you.

: )