Question

The sum of the digits of a two digit number is 13.If the digits are interchanged, and the resulting number is added to the original number, we get 143.What is the original number?​

Answer 1

Step-by-step 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