Question

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

Answer 1

Heya.

Let us work out with few numbers and get the answer

Number: 23

Sum of digits : 2+3=5

23-5= 18

It is divisible by 2 and 9

Number : 15

Sum of digits : 1+5=6

15-6 = 9

It is divisible by 9

So, the answer is d)9

We get the same answer if we take any other Numbers also.

Hope it helps! ^_^

Answer 2

Answer:  The correct option is (d) 9.

Step-by-step explanation:  Given that the sum of the digits of a number is subtracted from the number itself.

We are to find the number that divides the resulting number.

Let x and y represent the digits in ten's place and one's place respectively of the given number.

So, the number is

n = 10x + y.

Then, we have

$n-(x+y)\\\\=10x+y-x-y\\\\=9x.$

Therefore, the resulting number has two factors 9 and x. Since x is unknown, so the number that divides the resulting number will be 9.

Option (d) is CORRECT.