The sum of two digit number is . The number obtained by interchanging the order of digits of the given number, it exceeds the given number by . Find the number.

Let the digits at unit’s place be a and ten’s place be v, respectively. Thus, the number we need to find is .

As per the given question, the sum of the two digit number is . Thus, we have;

……………(i)

Upon interchanging the digit’s place, the new number will  be .

It is also given that, the new number obtained exceeds from the original number by . Therefore, we can write this as;

⇒

⇒

⇒

⇒

⇒ ………………….. (ii)

On solving equation (i) and (ii), we can find value of a and b.

Now, adding the equations (i) and (ii), we get;

⇒

⇒

⇒

⇒

Putting the value of a in the equation (i), we get value of b

⇒

⇒

Hence, the required number is,