In a number system , on dividing 11509 by a certain number , Mukesh gets 71 as quotient and 7 as remainder . What is the divisor ?

Options

A. A)132
B. B)172
C. C)182
D. D)162

Answer

To find the divisor in the given problem, we can use the formula that relates the dividend, divisor, quotient, and remainder:

\[ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} \]

Given:
- Dividend = 11509
- Quotient = 71
- Remainder = 7

We can rearrange the formula to solve for the divisor:

\[ \text{Divisor} = \frac{\text{Dividend} - \text{Remainder}}{\text{Quotient}} \]

Now, let's substitute the values into the formula step by step:

1. **Calculate Dividend - Remainder**:
\[ 11509 - 7 = 11502 \]

2. **Divide by Quotient**:
\[ \text{Divisor} = \frac{11502}{71} \]

3. **Perform the Division**:
\[ \text{Divisor} = 162 \]

Thus, the divisor is **162**.