Twenty is 0.25 percent of which number?

Introduction / Context:
This question checks comfort with very small percentages by asking you to reverse the usual operation. Instead of finding a percentage of a number, you are given the result and asked to recover the original number. Such reverse percentage problems are common in aptitude exams and strengthen your understanding of percentage as a fraction of 100.

Given Data / Assumptions:
- Let the unknown number be N.
- 0.25 percent of N equals 20.
- 0.25 percent means 0.25 out of 100.
- We need to find the value of N that satisfies this relationship.

Concept / Approach:
Percent literally means "per hundred". So 0.25 percent of N is (0.25 / 100) * N. The equation (0.25 / 100) * N = 20 can be solved to find N. It is often convenient to convert 0.25 percent to its decimal form 0.0025 and then divide the given value by this factor to obtain the original number.

Step-by-Step Solution:
Step 1: Express 0.25 percent as a decimal factor. 0.25 percent = 0.25 / 100 = 0.0025.Step 2: Write the relationship: 0.0025 * N = 20.Step 3: Solve for N by dividing both sides by 0.0025.Step 4: N = 20 / 0.0025.Step 5: Compute 20 / 0.0025. Since 0.0025 = 25 / 10,000, dividing 20 by 0.0025 gives 20 * (10,000 / 25) = 20 * 400 = 8,000.Step 6: Therefore N = 8,000.

Verification / Alternative check:
Check by computing 0.25 percent of 8,000 directly. First find 1 percent of 8,000, which is 80. Then 0.25 percent is one quarter of 1 percent, so it is 80 / 4 = 20. This matches the given result, confirming that the original number is 8,000.

Why Other Options Are Wrong:
- 10,000 would give 0.25 percent of 10,000 as 25, not 20.
- 5,000 would give 0.25 percent as 12.5, which is too small.
- 2,500 would give 0.25 percent as 6.25, which is even smaller and clearly does not match 20.

Common Pitfalls:
Students sometimes confuse 0.25 percent with 25 percent, which is a hundred times larger. Another mistake is to divide 20 by 0.25 instead of by 0.25 percent, forgetting to divide by 100 as well. Always convert the given percentage correctly into a decimal or fractional factor before forming the equation.

Final Answer:
The required number is 8,000.