Question

A number is subtracted from another number formed by interchanging the digits of the original number. What can you say about the difference obtained?

Answer 1

For the original number, we take:

$Tensdigit=aOnesdigit=b$

Hence,

$Originalnumber=(10\times a)+(1\times b)=10a+b$

Now, interchanging the digits, we get the new number as:

$Tensdigit=bOnesdigit=a$

Hence,

$Newnumber=(10\times b)+(1\times a)=10b+a$

Subtracting the original number from the new number, we get:

$Difference=(10b+a)–(10a+b)=(10b–b)–(10a–a)=9b–9a=9(b–a)$

As both b and a are whole numbers, (b – a) will also be a whole number.

Hence, the difference will always be a multiple of 9.