Question

On dividing$2272$as well as$875$by a $3$-digit number $\text{N}$, we get the same remainder in each case. The sum of the digits of $\text{N}$ is

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

The correct option is A

$10$

By division algorithm, we know that -

$\text{Dividend = (divisor×quotient)+remainder}$

Let the remainder in each case be$\text{"r"}$, quotient when$2272$ divided by$\text{N}$ be $\text{"m"}$ and quotient when divided$875$divided by $\text{N}$be $\text{"n"}$.

Using the division algorithm,

$$\begin{gathered} \text{2272 = Nm+r ------------------}\left(i\right) \\ 875=Nn+r------------------\left(ii\right) \end{gathered}$$

Subtracting equation (ii) from (i) we wiil get -

$$\begin{gathered} \text{1397 = N(m-n)} \\ \text{11×127 = N(m-n)} \end{gathered}$$

Since, a three-digit number is $127$, therefore the value of $\text{N}$ is $127.$

The sum of digits of $\text{N}$ = $1+2+7=10$

Hence, the correct option is $A$.