(Q18).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?

Let the digit in units place be x

and the digit in tens place be y

then the value of the number = y + x

Number obtained by reversing the digits = x + y

By problem,

(y + x) + (x + y) =

and x – y =

⇒ x – y = and x – y =

⇒ x + y = and x – y =

Solving these two equations

x + y = 6

x – y = 2

(+) x =

x =
=

Substituting x = in x + y = 6

we get + y = 6 ⇒ y =

Substituting x, y values in equations (10y + x) & (10x + y),

We get 10y + x

= 10() + = + =

and 10x + y = 10() +

= + =

∴ The number is or

Thus we have two such numbers.