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 \( N \).

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

**Hint:** Remember that when a number is divided by another, it can be expressed in the form of a multiple of the divisor plus the remainder.

### Step 2: Find the relationship with 35
Next, we need to find the remainder when \( N \) is divided by 35. Since we have expressed \( N \) in terms of 280, we can substitute it into the equation:
\[ N = 280k + 115 \]

### Step 3: Simplify the expression modulo 35
Now, we can find \( N \mod 35 \):
1. First, we need to calculate \( 280 \mod 35 \):
\[ 280 \div 35 = 8 \quad \text{(since } 35 \times 8 = 280\text{)} \]
Therefore, \( 280 \mod 35 = 0 \).

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

### Step 4: Combine the results
Since \( 280k \mod 35 = 0 \), we have:
\[ N \mod 35 = (280k + 115) \mod 35 = (0 + 10) \mod 35 = 10 \]

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