What is the value of 20% of 500% of 50?

Introduction / Context:
This is a basic but important percentage composition problem. It involves applying one percentage to the result of another percentage applied to a number. Questions of this type build comfort with nested percentage operations and reinforce the fact that percentage of a percentage is equivalent to multiplication of their decimal forms.

Given Data / Assumptions:
We need to compute 20 percent of 500 percent of 50.
All percentages are taken in the usual sense: x percent means x / 100 times the quantity.
The operations are applied sequentially: first compute 500 percent of 50, then take 20 percent of that result.

Concept / Approach:
To find 500 percent of 50, we note that 500 percent corresponds to 500 / 100 = 5 times the original number. So 500 percent of 50 is 5 * 50. After that, to find 20 percent of the result, we multiply by 20 / 100 = 0.20. Overall, the expression is 0.20 * (5 * 50). We can also combine the percentages into a single factor: (20 / 100) * (500 / 100) times 50. This equals (0.20 * 5) * 50.

Step-by-Step Solution:
First compute 500 percent of 50. 500 percent = 500 / 100 = 5 as a multiplier. So 500 percent of 50 = 5 * 50 = 250. Now compute 20 percent of this result. 20 percent = 20 / 100 = 0.20. So 20 percent of 250 = 0.20 * 250. Compute 0.20 * 250 = 50. Therefore, 20 percent of 500 percent of 50 equals 50.

Verification / Alternative check:
Alternatively, we can combine all operations in one expression: (20 / 100) * (500 / 100) * 50. This equals (0.20 * 5) * 50 = 1 * 50 = 50. Since both step by step computation and combined computation give the same result, we are confident that the answer is correct. This method also shows that percentages behave like ordinary multiplicative factors when chained together.

Why Other Options Are Wrong:
A value of 0.5 would arise from misplacing decimal points or mistakenly dividing instead of multiplying. A result of 5000 would come from multiplying 500 percent and 50 directly and then adding an extra factor, which is incorrect. A result of 500 would correspond to 20 percent of 2500 or 200 percent of 250, not the expression given here. Only 50 fits the correct chain of operations as described in the problem.

Common Pitfalls:
Learners sometimes misinterpret 500 percent as 500 divided by 100 twice, or they forget that 500 percent means five times the number. Others may apply 20 percent to the original 50 directly, ignoring the intermediate result. To avoid these issues, follow the order of operations exactly as stated: first apply 500 percent to 50, then apply 20 percent to that result. Converting each percentage to a decimal multiplier and multiplying in the correct order keeps the process clear and error free.

Final Answer:
The value of 20 percent of 500 percent of 50 is 50.