Question

the sum of the digits of a 2-digits number is 13 the number formed by interchanging the digits is 45.find the original number
​

Answer 1

Heya!!

The Question should be like this.

The sum of the digits of a two digit number is 13. and the number formed by interchanging the digits is Either less or more then the orginal number by 45.

Case1:- Number Formed by interchanging the digits is More than the original number.

Let the digits of that number be x and y

According to the given Question

x + y = 13 ... Equation i

10y + x = 45 + 10x + y

9y - 9x = 45

9 ( y - x ) = 9 × 5

y - x = 5 ... Equation ii

Now, Add both The Equations we have.

2y = 18

2y = 9 × 2

y = 9

Put value of y in Equation ii we have.

9 - x = 5

x = 4

So, The original number is 49

Case 2:- The number formed by interchanging the digits is less then the original by 45

According to the given Question.

x + y = 13 ... Equation i

10y + x = 10x + y - 45

x - y = 5 ... Equation ii

Now, Add both the Equations we have.

2x = 18

x = 9

Now, put value of x in Equation ii we have

9 - y = 5

y = 4

So, the original number is 94