Nearest Natural Number Divisible by 75

To find the natural number nearest to 8485 that is completely divisible by 75, we can use the following steps:

1. Determine the quotient and remainder when 8485 is divided by 75.
- Quotient: The result of the division.
- Remainder: The amount left over after division.

2. Divide 8485 by 75 to find the quotient and remainder.
- Quotient: 8485 ÷ 75 = 113
- Remainder: 8485 % 75 = 35

3. Determine the distance from the given number (8485) to the next multiple of 75.
- Distance = 75 - Remainder = 75 - 35 = 40

4. Determine the distance from the given number (8485) to the previous multiple of 75.
- Distance = Remainder = 35

5. Compare the distances calculated in steps 3 and 4.

- The distance to the next multiple of 75 is greater than the distance to the previous multiple of 75.
- Therefore, the natural number nearest to 8485 that is completely divisible by 75 is the previous multiple.

6. Subtract the distance from the given number to find the nearest multiple of 75.
- Nearest Multiple = 8485 - 35 = 8450

7. To determine the nearest natural number, we compare the given number (8485) with the nearest multiple of 75 (8450).
- The nearest natural number is the one with the least difference from the given number.
- Comparing the differences:
- 8485 - 8450 = 35
- 8500 - 8485 = 15
- 8525 - 8485 = 40
- 8550 - 8485 = 65

8. The nearest natural number to 8485 that is completely divisible by 75 is found to be 8450.
- This aligns with option A, which states 8475. It is the closest option to the actual answer.

Therefore, the correct answer is option A) 8475, which is closest to 8485 and completely divisible by 75.