Evaluate 56% of 225 plus 20% of 150, given that 56% of 225 + 20% of 150 = ? - 109. Find the value of '?'.

Introduction / Context:
This question combines percentage calculations with a simple linear equation involving an unknown represented by a question mark. You are asked to evaluate two percentage expressions, add them, and then relate the total to an expression of the form ? - 109. Problems like this appear frequently in arithmetic aptitude to test accurate percentage computation and equation solving skills.

Given Data / Assumptions:

• We must compute 56% of 225.
• We must compute 20% of 150.
• The equation is 56% of 225 + 20% of 150 = ? - 109.
• We must find the value of the unknown quantity ?.
• No rounding is needed because the numbers chosen give exact decimal results.

Concept / Approach:
The first step is to evaluate each percentage term. We can convert 56% and 20% to fractions or decimals and multiply by the respective numbers. Once we have these two values, we add them together to find the left side of the equation. Then we use basic algebra to solve for ?, since ? - 109 must equal that computed sum. This direct approach keeps the problem simple and mechanical.

Step-by-Step Solution:
Step 1: Compute 56% of 225.Step 2: 56% of 225 = (56/100) * 225.Step 3: 225 * 56/100 = 2.25 * 56 = 126.Step 4: Next, compute 20% of 150.Step 5: 20% of 150 = (20/100) * 150 = 0.2 * 150 = 30.Step 6: Add the two results: 126 + 30 = 156.Step 7: According to the equation, 56% of 225 + 20% of 150 = ? - 109.Step 8: So we have 156 = ? - 109.Step 9: Solve for ?: ? = 156 + 109 = 265.

Verification / Alternative check:
We can verify by substituting ? = 265 back into the equation. The right side becomes 265 - 109 = 156. The left side we have already computed as 126 + 30 = 156. Since both sides match, the equation holds true and the value ? = 265 is confirmed. There are no approximations involved, so the result is exact.

Why Other Options Are Wrong:
Option 264 would give 264 - 109 = 155, which does not match the left side, 156. Option 220 would give 220 - 109 = 111, which is far from 156. Option 241 would give 241 - 109 = 132, again not matching the left side. The option 265 correctly satisfies the equation, but in the original list the correct numerical value is not among the main numeric options, so the best match in the provided choices is "None". Hence, "None" is the correct option since the actual value 265 is not one of the three given numeric alternatives.

Common Pitfalls:
Some learners miscalculate 56% of 225 by incorrectly splitting the percentage or misplacing the decimal. Others may forget to include 109 when solving for ? and mistakenly set ? equal to 156 instead of 265. A few may also misread the equation and subtract in the wrong direction. To avoid these mistakes, carefully compute each percentage, write down the intermediate sum, and then solve the equation step by step, ensuring that the operations on both sides of the equation are correct.

Final Answer:
The value of the unknown '?' is 265, so the correct choice from the options is "None".