A number when divided by 123 leaves remainder 83. If the same number is divided by 41, the remainder will be-

Options

A. 0
B. 1
C. 40
D. 83

Answer

To solve the problem step by step, we will follow these instructions:

1. **Understand the problem**: We are given that a number when divided by 123 leaves a remainder of 83. We need to find the remainder when the same number is divided by 41.

2. **Set up the equation**: Let the number be \( x \). According to the problem, when \( x \) is divided by 123, it leaves a remainder of 83. This can be expressed mathematically as:
\[ x = 123k + 83 \]
where \( k \) is some integer.

3. **Substitute and simplify**: We need to find the remainder of \( x \) when divided by 41. We can substitute the expression for \( x \) into the division by 41:
\[ x = 123k + 83 \]
Now, we will find \( 123 \mod 41 \) and \( 83 \mod 41 \).

4. **Calculate \( 123 \mod 41 \)**:
\[ 123 \div 41 = 3 \quad \text{(since \( 41 \times 3 = 123 \))} \]
So,
\[ 123 \mod 41 = 0 \]

5. **Calculate \( 83 \mod 41 \)**:
\[ 83 \div 41 = 2 \quad \text{(since \( 41 \times 2 = 82 \))} \]
Therefore,
\[ 83 - 82 = 1 \quad \Rightarrow \quad 83 \mod 41 = 1 \]

6. **Combine the results**: Since \( 123 \mod 41 = 0 \), we can simplify our expression:
\[ x \mod 41 = (123k + 83) \mod 41 = (0 + 1) \mod 41 = 1 \]

7. **Conclusion**: The remainder when the number \( x \) is divided by 41 is:
\[ \text{Remainder} = 1 \]