Question

The digits of a two-digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number, the sum is 143. What is the original number?

Answer 1

Number is `58` or `85`.

Explanation:

As te digits of two digit number differ by `3`, there are two possibilities. One the unit digit be `x` and tens digit be `x+3`, and two that tens digit is `x` and unit digit is `x+3`.

In first case, if unit digit be `x` and tens digit is `x+3`, then number is `10(x+3)+x=11x+30` and on interchanging numbers, it will become `10x+x+3=11x+3`.

As sum of numbers is `143`, we have

`11x+30+11x+3=143` or `22x=110` and `x=5`.

and number is `58`.

Observe that if it is reversed i.e it becomes `85`, then sum of two again will be `143`.

Hence number is `58` or `85`