In the expression 75 percent of 450 plus an unknown percentage of 560 equals 600, find the unknown percentage of 560 that makes the statement true.

Introduction / Context:
This question tests your ability to handle an equation involving percentages of different numbers. You are given one known percentage term, one unknown percentage term, and their sum. You must isolate the unknown percentage and compute its value carefully using basic algebra and percentage skills.

Given Data / Assumptions:

• 75 percent of 450 is known.
• Let the unknown percentage of 560 be p percent.
• The equation is: 75 percent of 450 + p percent of 560 = 600.
• We solve for p and then match it to one of the given options.

Concept / Approach:
First compute 75 percent of 450. Then subtract this from 600 to find the remaining value that must be contributed by p percent of 560. Once you know the absolute contribution from 560, calculate p by treating it as (p / 100) * 560. Rearranging the equation gives p = (required value / 560) * 100. The key idea is setting up and solving a straightforward linear equation in p.

Step-by-Step Solution:
Step 1: Compute 75 percent of 450 = (75 / 100) * 450 = 0.75 * 450 = 337.5. Step 2: The total required is 600, so the remaining part from the second term is 600 − 337.5 = 262.5. Step 3: Let p be the unknown percentage. Then (p / 100) * 560 = 262.5. Step 4: Solve for p: p = (262.5 * 100) / 560. Step 5: Compute 262.5 / 560 = 0.46875, so p = 0.46875 * 100 = 46.875. Step 6: Therefore the unknown percentage is 46.875 percent.

Verification / Alternative check:
Check by substitution: 46.875 percent of 560 is (46.875 / 100) * 560 = 0.46875 * 560 = 262.5. Adding 337.5 and 262.5 gives 600, confirming the correctness of the computed percentage.

Why Other Options Are Wrong:

• 52.385% would make the second term too large and the total more than 600.
• 42.155% and 40.555% would yield smaller contributions from 560, so the sum would be less than 600.

Common Pitfalls:
Errors often occur if you round too early or mis-handle decimal multiplication. Another common mistake is to divide 560 by 262.5 incorrectly. Writing each algebraic step clearly and simplifying with care helps avoid these issues.

Final Answer:
The unknown percentage of 560 is 46.875%.