A leading chocolate producing company produces 'abc' chocolates per hour (abc is a three digit positive number). In how many hours it will produce 'abcabc' chocolates?

Options

A. abc
B. 101
C. 1001
D. can't be determined

Answer

To solve the problem of how many hours it will take for a chocolate company to produce 'abcabc' chocolates when it produces 'abc' chocolates per hour, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Numbers**:
- Let 'abc' be a three-digit number. This can be expressed as \( N \) where \( N = 100a + 10b + c \) (with \( a, b, c \) being the digits of the number).
- The number 'abcabc' can be represented as \( 1000N + N = 1001N \).

2. **Production Rate**:
- The company produces \( N \) chocolates per hour.

3. **Total Production Calculation**:
- To find out how many hours it will take to produce \( 1001N \) chocolates, we can use the formula:
\[ \text{Total Hours} = \frac{\text{Total Chocolates}}{\text{Chocolates per Hour}} = \frac{1001N}{N} \]

4. **Simplifying the Equation**:
- When we simplify the equation:
\[ \text{Total Hours} = \frac{1001N}{N} = 1001 \]

5. **Conclusion**:
- Therefore, it will take **1001 hours** to produce 'abcabc' chocolates.

### Final Answer:
The company will take **1001 hours** to produce 'abcabc' chocolates.

---