Simplify and evaluate the expression 43% of 616.6 plus 37% of 217, and find the resulting numerical value correct to three decimal places.

Introduction / Context:
This question is designed to test your understanding of percentage calculations and addition of decimal numbers. Such problems commonly appear in data interpretation and basic arithmetic sections of aptitude exams. The key is to convert the given percentages into decimal multipliers and then perform accurate multiplication and addition with decimals.

Given Data / Assumptions:

• We need to compute 43 percent of 616.6.
• We also need to compute 37 percent of 217.
• The final answer is the sum of these two quantities.
• Percent means per hundred, so 43 percent is 43 / 100 and 37 percent is 37 / 100.

Concept / Approach:
To find a percentage of a number, we multiply the number by the percentage written as a fraction over 100 or as a decimal. That is, A percent of B equals (A / 100) * B. After calculating each part separately, we add the results to obtain the total. Careful handling of decimal places ensures the final answer is accurate to three decimal places, as reflected in the options.

Step-by-Step Solution:
Compute 43 percent of 616.6: 43 / 100 * 616.6 = 0.43 * 616.6.0.43 * 616.6 = 265.138.Compute 37 percent of 217: 37 / 100 * 217 = 0.37 * 217.0.37 * 217 = 80.29.Now add the two results: 265.138 + 80.29.265.138 + 80.29 = 345.428.

Verification / Alternative check:
A quick check can be done by approximating. Forty percent of about 600 is around 240, and three percent more adds roughly 18 to 20, giving around 260. Similarly, 37 percent of a little more than 200 is roughly 74 to 80. Adding approximate values 260 and 80 gives about 340, which is close to 345. This confirms that 345.428 is in a reasonable range. Recomputing the exact decimal multiplications confirms the precise answer.

Why Other Options Are Wrong:
354.428 and 344.428 differ from the exact sum by 9 or 1 units, which arises from incorrect multiplication or from rounding errors. 364.428 and 335.428 are even further off and indicate more serious miscalculations, such as interchanging the percentages or misplacing the decimal point. Only 345.428 matches the accurate calculation.

Common Pitfalls:
Typical mistakes include misinterpreting 43 percent as 4.3 or 0.043, and losing track of decimal places while multiplying. Sometimes candidates forget to convert the percentages to fractions over 100 and instead divide the base number by the percentage. Writing each step clearly and keeping two or three decimal places throughout helps preserve accuracy.

Final Answer:
The value of 43% of 616.6 plus 37% of 217 is 345.428.