If a quantity of 16 is compared with 225, 16 is equal to what percent of 225?

Introduction / Context:
This question checks the basic idea of expressing one number as a percentage of another number. Problems of this type are very common in data interpretation, percentage chapters in quantitative aptitude, and everyday calculations like test scores or growth rates.

Given Data / Assumptions:

First quantity (part) = 16.
Second quantity (whole) = 225.
We need to find 16 as a percentage of 225.
Standard percentage formula is used, with normal rounding to two decimal places where needed.

Concept / Approach:
To find what percent one number is of another, we use:
percentage = (part / whole) * 100 Here the part is 16 and the whole is 225. After forming the fraction, we multiply by 100 to convert the value into percent form. Accurate division is important to get the correct answer to two decimal places.

Step-by-Step Solution:
Step 1: Write the required percentage as (16 / 225) * 100. Step 2: First compute 16 / 225. This is approximately 0.071111... Step 3: Multiply this by 100 to convert it to percent: 0.071111... * 100. Step 4: 0.071111... * 100 = 7.1111... which rounds to about 7.11%. Step 5: Therefore, 16 is approximately 7.11% of 225.

Verification / Alternative check:
We can verify by reversing the calculation. Take 7.11% of 225 and see if it is close to 16. Compute (7.11 / 100) * 225. First 7.11 / 100 = 0.0711. Then 0.0711 * 225 is approximately 15.9975, which rounds to 16. The small difference is due to rounding the percentage to two decimal places, and the result confirms that 7.11% is correct.

Why Other Options Are Wrong:
6.87% gives (6.87 / 100) * 225 which is less than 16.
7.58% gives a value slightly more than 16 when applied to 225.
8.25% is much higher and gives a significantly larger value than 16.
5.50% produces a much smaller value when multiplied by 225.

Common Pitfalls:
Learners sometimes compute 225 / 16 instead of 16 / 225, which inverts the relationship. Forgetting to multiply by 100 at the end or rounding too early in the division can also lead to incorrect answers. It is helpful to remember that when the part is smaller than the whole, the resulting percentage should be less than 100% and, in this case, clearly less than 10% because 16 is much smaller than 225.

Final Answer:
Sixteen is 7.11% of 225 (approximately).