If two numbers x and y separately divided by a number d, remainders obtained are 4375 and 2986 respectively. If the sum of the numbers 1.e (x+y) is divided by the same number d remainder obtained is 2361. The value of number d is

Options

A. 7361
B. 5000
C. 4000
D. 2542

Answer

To solve the problem, we need to find the value of the number \( d \) given the remainders when two numbers \( x \) and \( y \) are divided by \( d \), and the remainder when their sum \( x + y \) is divided by \( d \).

### Step-by-Step Solution:

1. **Understanding the Remainders:**
- When \( x \) is divided by \( d \), the remainder is \( 4375 \).
- When \( y \) is divided by \( d \), the remainder is \( 2986 \).
- When \( x + y \) is divided by \( d \), the remainder is \( 2361 \).

2. **Expressing the Numbers:**
- We can express \( x \) and \( y \) in terms of \( d \):
\[ x = kd + 4375 \quad \text{(for some integer } k\text{)} \]
\[ y = md + 2986 \quad \text{(for some integer } m\text{)} \]

3. **Finding the Sum:**
- The sum \( x + y \) can be expressed as:
\[ x + y = (kd + 4375) + (md + 2986) = (k + m)d + (4375 + 2986) \]
- Simplifying the constant part:
\[ 4375 + 2986 = 7361 \]
- Therefore, we have:
\[ x + y = (k + m)d + 7361 \]

4. **Using the Remainder of the Sum:**
- When \( x + y \) is divided by \( d \), the remainder is given as \( 2361 \):
\[ (k + m)d + 7361 \equiv 2361 \mod d \]
- This implies:
\[ 7361 \equiv 2361 \mod d \]

5. **Finding the Difference:**
- We can find the difference:
\[ 7361 - 2361 = 5000 \]
- Therefore, we have:
\[ 7361 - 2361 = 5000 \equiv 0 \mod d \]
- This means \( d \) must be a divisor of \( 5000 \).

6. **Conclusion:**
- The value of \( d \) is \( 5000 \).

### Final Answer:
The value of \( d \) is \( 5000 \).