What percentage of 85 is equal to 120?

Introduction / Context:
This is a straightforward percentage problem where we express one number as a percentage of another. Such questions directly check the basic skill of converting a ratio into a percentage, which is fundamental in many areas of quantitative aptitude, data interpretation and everyday calculations.

Given Data / Assumptions:
- We have two numbers: 120 and 85.
- We need to find what percentage 120 is of 85.

Concept / Approach:
To find what percent one number A is of another number B, we use the formula:
Percentage = (A / B) * 100. Here, A is 120 and B is 85. We simply compute the fraction 120 / 85 and multiply by 100 to get the required percentage. The result will be more than 100 percent because 120 is greater than 85.

Step-by-Step Solution:
Let the required percentage be p. Then p = (120 / 85) * 100. First compute the fraction: 120 / 85. 120 / 85 simplifies to 24 / 17. Now compute (24 / 17) * 100. 24 * 100 = 2400. So p = 2400 / 17. Compute 2400 / 17 which is approximately 141.17 percent.

Verification / Alternative check:
We can check reasonableness. Since 85 * 1.4 = 119, which is very close to 120, we expect the answer to be close to 140 percent. More precisely, 85 * 1.4117 is roughly 120. That matches the calculated percentage of about 141.17 percent and confirms the correctness of the answer.

Why Other Options Are Wrong:
133.33% and 135%: These values are too small; they would produce numbers significantly less than 120 when multiplied by 85 as percents.
145.54% and 139.29%: These are close but still do not match the exact ratio 2400 / 17, which is approximately 141.17%.

Common Pitfalls:
A common error is to compute 85 as a percentage of 120 instead of the other way around, which would invert the fraction. Another pitfall is rounding too early or trying to handle the calculation mentally without simplifying the fraction first. Writing the fraction clearly as 24 / 17 and then dividing helps reach the accurate value.

Final Answer:
The number 120 is approximately 141.17 percent of 85.