Question

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

(A) 2
(B) 5
(C) 8
(D) 9​

Answer 1

Answer:

• The resulting number is always divisible by 9.

Step-by-step explanation:

Let us assume:

• Tens digit of a number be x.
• Ones digit of a number be y.
• Then, Number = 10x + y

Given that:

• The sum of the digits of a number is subtracted from the number.

i.e., (10x + y) - (x + y)

To Find:

• The resulting number is always divisible by

Solving (10x + y) - (x + y):

= 10x + y - x - y

= 10x - x + y - y

= 9x

The factor of 9x is 9 and x.

So, we can say that the resulting number is always divisible by 9.

Answer 2

Given :-

The sum of the digits of a number is subtracted from the number.

To Find :-

Number will be divisible by

Solution :-

Let the tens be x and ones be y

10x + y

Now

10x + y - x - y

10 - x + y - y

9x + 0

9x

Since 9 divisible by x.

Number = 9