What value should replace the question mark in the expression: 52.5% of 800 + 30.5% of 2800 = ? + 87.30 ?

Introduction / Context:
This question combines percentage calculations with a simple linear equation. We are given an expression where two percentage terms are added and the sum is split into an unknown part plus a constant. The task is to compute the actual numerical value of the percentage expressions and then isolate the missing term. This kind of question is common in quantitative aptitude and helps build accuracy with multi-step arithmetic expressions.

Given Data / Assumptions:

First term: 52.5% of 800.
Second term: 30.5% of 2800.
Their sum equals an unknown value plus 87.30.
We need to find the value of the unknown term represented by question mark.
Percentages are interpreted as simple hundred-based percentages with standard arithmetic.

Concept / Approach:
First compute each percentage value by converting the percentage into decimal and multiplying by the base number. Then add the two results to obtain the left side total. According to the given equation, that total equals the unknown term plus 87.30. We then subtract 87.30 from the total to get the unknown. This is a straightforward use of percentage calculation followed by a simple rearrangement of an equation.

Step-by-Step Solution:
Step 1: Compute 52.5% of 800. 52.5% = 52.5 / 100 = 0.525. 0.525 * 800 = 420. Step 2: Compute 30.5% of 2800. 30.5% = 30.5 / 100 = 0.305. 0.305 * 2800 = 854. Step 3: Add both results to get the left side of the equation. Left side total = 420 + 854 = 1,274. Step 4: Use the given relationship. 1,274 = ? + 87.30. Step 5: Subtract 87.30 from both sides to solve for the unknown. ? = 1,274 - 87.30. ? = 1,186.70. Hence, the missing value is 1,186.70.

Verification / Alternative check:
To verify, substitute 1,186.70 back into the original expression. The right side becomes 1,186.70 + 87.30 = 1,274. This matches the left side value calculated as 420 + 854 = 1,274. Since both sides are equal after substitution, the value 1,186.70 satisfies the equation and is correct.

Why Other Options Are Wrong:
1,096.30 and 1,124.20 would give right side totals of 1,183.60 and 1,211.50 respectively, both less than 1,274.
1,226.70 would give a total of 1,314, which is greater than 1,274.
1,274.00 would imply the other term is zero, but 87.30 is clearly present on the right side, so this cannot be correct.

Common Pitfalls:
Some learners misread 52.5% or 30.5% as 0.52 or 0.30 instead of 0.525 and 0.305. Others might forget to multiply by 100 when converting to decimal or misplace the decimal point. Another frequent error is to add the 87.30 instead of subtracting it when solving for the unknown term. Carefully converting percentages and keeping track of the equation structure prevents these mistakes.

Final Answer:
The value that should replace the question mark is 1,186.70.