Find the value of 45% of 750 minus 25% of 480.

Introduction / Context:
This is a direct numerical computation involving two separate percentage calculations and a subtraction. It tests calculation accuracy and comfort with basic percentages. Questions like this help build speed and confidence with mental arithmetic or quick written calculation, which is important in many competitive exams where time is limited.

Given Data / Assumptions:

• We must calculate 45% of 750.
• We must calculate 25% of 480.
• The required value is the difference: (45% of 750) minus (25% of 480).
• No rounding is involved because all values are exact.

Concept / Approach:
The approach is to evaluate each percentage separately and then subtract. Percentages can be converted to fractions for simpler computation. For example, 45% is 45/100, and 25% is 25/100. We multiply these fractions by the respective numbers to find the percentage values. Breaking down the numbers into factors also makes calculations simpler. After both results are obtained, we subtract the second from the first to get the final answer.

Step-by-Step Solution:
Step 1: Compute 45% of 750.Step 2: 45% of 750 = (45/100) * 750.Step 3: Simplify 750 * 45/100 = 7.5 * 45 = 337.5.Step 4: Next, compute 25% of 480.Step 5: 25% of 480 = (25/100) * 480.Step 6: Simplify 480 * 25/100 = 4.8 * 25 = 120.Step 7: Now find the difference: 337.5 - 120.Step 8: 337.5 - 120 = 217.5.Step 9: Therefore, the required value is 217.50.

Verification / Alternative check:
We can check our calculations in another way by using fraction breakdown. Note that 45% of 750 can be written as (9/20) * 750. Since 750 / 20 = 37.5, 37.5 * 9 = 337.5, which matches our earlier value. Similarly, 25% of 480 is (1/4) * 480 = 120. Subtracting 120 from 337.5 again gives 217.5. As both methods agree, the result is confirmed.

Why Other Options Are Wrong:
Option 337.50 is just the value of 45% of 750 and ignores the subtraction of 25% of 480. Option 376.21 is not supported by any reasonable calculation and appears to be a random value. Option 120 is only the value of 25% of 480 and not the difference of the two quantities. Option 185.50 does not match the correct subtraction result. Only 217.50 is consistent with the step-by-step percentage calculations.

Common Pitfalls:
Some learners mistakenly add the two percentage values instead of subtracting, or they mix up which number to take each percentage from. Others misplace the decimal point when multiplying by percentage fractions, for example, treating 45% as 4.5 instead of 0.45. To avoid these errors, clearly write each operation, convert percentages to fractions or decimals carefully, and double-check the final subtraction.

Final Answer:
The value of 45% of 750 minus 25% of 480 is 217.50.