Question

the sum of the digits of a number is subtracted from a number , the resulting number is always divisible by 
a)2
b)5
c)8
d)9
and why ? show the working

Answer 1

Hey there! :)

Let the number be xy , that is 10x+y .

Given, Sum of digits = x + y.

Question : The sum of digits of a number is subtracted from a number, the resulting number is always divisible by.

Number - Sum of digits

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

= 10x + y - x - y

$= 10x - x + \cancel{ y }- \cancel{y}$

= 9x .

So , 9x has factors 9 & x. Therefore, 9x is always divisible by 9 .

The sum of the digits of a number is subtracted from a number , the resulting number is always divisible by 9 .

Answer 2

Answer:

IN ABOVE IMAGE

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