Question

The sum of the digits of a 3-digit number is subtracted from the number. The resulting number is always.
(a) Divisible by 6
(b) Not divisible by 6
(c) Divisible by 9
(d) Not divisible by 9

Answer 1

Hint: For solving this question we will assume $abc$ to be a 3-digit number. After that, we will proceed as per the information given in the question and check that when we subtract the sum of the digits from the number then the resulting number is divisible by 9, 6 or it is not divisible.

Complete step-by-step answer:
There is a 3-digit number and when we subtract the sum of digits of the 3-digit number from the 3-digit number. And we have to check whether the result after subtraction is divisible by 9, 6 or not.
Now, let the 3-digit number be $abc$ where, $a$ is any natural number from 1 to 9, $b$ and $c$ are any whole numbers from 0 to 9.
Now, as the 3-digit number is $abc$ . Then,
$abc=100a+10b+c$
Sum of the digits of a 3-digit number $abc=a+b+c$ .
Now, as per the given data, we have to subtract the sum of the digits of the 3-digit number from the 3-digit number. Then,
$\begin{align}
  & abc-\left( a+b+c \right) \\
 & \Rightarrow 100a+10b+c-a-b-c \\
 & \Rightarrow 99a+9b \\
 & \Rightarrow 9\left( 11a+b \right) \\
\end{align}$
Now, as the result after subtracting the sum of the digits of 3-digit number from the number is equal to $9\left( 11a+b \right)$ and it is evident that the result after subtraction is divisible by 9 and not divisible by 6.
Thus, we can say that when the sum of the digits of a 3-digit number is subtracted from the number. Then the resulting number will be always divisible by 9.
Hence, (c) is the correct option.

Note: Here, the student should first understand what is asked in the question and we should be aware of the given options before we start solving the problem. After that, we should use basic arithmetic techniques and proceed as per the given data to get the correct answer. Moreover, we should be careful while selecting the option.