A number when divided by 280 leaves 115 as remainder. When the same number is divided by 35, the remainder is

Options

A. 10
B. 15
C. 17
D. 20

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Set up the equation based on the given information
According to the problem, when the number \( x \) is divided by 280, it leaves a remainder of 115. This can be expressed mathematically as:
\[ x = 280k + 115 \]
where \( k \) is some integer (the quotient when \( x \) is divided by 280).

### Step 2: Find the relation when the number is divided by 35
Now, we need to find the remainder when \( x \) is divided by 35. We can substitute the expression for \( x \) from Step 1 into the equation:
\[ x = 280k + 115 \]

### Step 3: Simplify \( x \) modulo 35
Next, we will simplify \( x \) modulo 35. We can start by simplifying each term in the equation:
1. **Calculate \( 280 \mod 35 \)**:
\[ 280 \div 35 = 8 \quad \text{(since \( 35 \times 8 = 280 \))} \]
Thus, \( 280 \mod 35 = 0 \).

2. **Calculate \( 115 \mod 35 \)**:
\[ 115 \div 35 = 3 \quad \text{(since \( 35 \times 3 = 105 \))} \]
The remainder when 115 is divided by 35 is:
\[ 115 - 105 = 10 \]
Therefore, \( 115 \mod 35 = 10 \).

### Step 4: Combine results to find \( x \mod 35 \)
Now substituting back into our equation for \( x \):
\[ x \mod 35 = (280k + 115) \mod 35 \]
Since \( 280 \mod 35 = 0 \), we have:
\[ x \mod 35 = (0 + 115) \mod 35 = 10 \]

### Conclusion
Thus, the remainder when the number \( x \) is divided by 35 is:
\[ \boxed{10} \]

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