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,