Question

The sum of digits of a two digit number is 3. If 9 is added to the number, the digits are reversed. Find the number.​

Answer 1

Let the digit at the ones place be y and the digit at the tens place be x . Then ,

Original Number = 10x + y ………..(1)

In the new number , the digits are reversed . So, x becomes the digit at the ones place and y becomes the digit at the tens place. So,

New Number = 10y + x

According to question,

Original Number - New Number = 9

=> (10x + y) - (10y + x) = 9

=> 10x + y - 10y - x = 9

=> 9x - 9y = 9

=> x - y = 1 …..(2)

It is given that :

x + y = 3 ……..(3)

Adding (2) and (3) , we get

2x = 4

=> x = 2

Putting x = 2 in (3) , we get

2 + y = 3

=> y = 1

Putting x = 2 and y = 1 in (1) , we get

Original Number = 10(2) + 1

=> Original Number = 20 + 1

=> Original Number = 21

Hence , the required number is 21 .