Calculate the value of 614 percent of 1600 plus 1212 percent of 800.

Introduction / Context:
This question is a direct computation involving large percentages. It tests the ability to convert high percentage values into their decimal or fractional equivalent and to work carefully with multiplication. Even though the percentages look large, the method is exactly the same as for smaller percentages.

Given Data / Assumptions:
First term: 614 percent of 1600. Second term: 1212 percent of 800. We must find the sum of these two terms. All values are positive and expressed in the same unit.

Concept / Approach:
To compute P percent of a number N, use the formula P/100 * N. So 614 percent of 1600 is (614/100) * 1600, and 1212 percent of 800 is (1212/100) * 800. We evaluate each expression separately and then add the results. Using fraction simplification makes the arithmetic cleaner.

Step-by-Step Solution:
Compute 614 percent of 1600: 614 percent of 1600 = (614 / 100) * 1600. Simplify: 1600 / 100 = 16, so this becomes 614 * 16. Compute 614 * 16 = 614 * 10 + 614 * 6 = 6140 + 3684 = 9824. Now compute 1212 percent of 800: 1212 percent of 800 = (1212 / 100) * 800. Simplify: 800 / 100 = 8, so this becomes 1212 * 8. Compute 1212 * 8 = 9696. Now add both contributions: 9824 + 9696. Sum = 19520. Therefore the required value is 19520.

Verification / Alternative check:
As a check, we can factor out 16 from both terms using a different grouping. Write 1600 as 16 * 100 and 800 as 16 * 50. Then 614 percent of 1600 is 6.14 * 1600 and 1212 percent of 800 is 12.12 * 800. Expressing 6.14 * 1600 as 614 * 16 and 12.12 * 800 as 1212 * 8 recovers the same intermediate numbers. Repeating the sums confirms that the total is 19520. Any change in arrangement of multiplication gives the same final result.

Why Other Options Are Wrong:
The options 15600, 17840, 21600, and 18400 are all plausible looking large numbers but do not match the exact arithmetic. A quick check of 9824 plus 9696 clearly yields 19520. Any other sum is due to either a miscalculated product or an incorrect handling of percentage conversion.

Common Pitfalls:
Learners sometimes treat 614 percent as 6.14 instead of 6.14 as a multiplier, or drop the extra factor of 100 by mistake. Another pitfall is adding percentages before multiplying without checking that the bases are the same. Systematically converting each percentage to a fraction and computing step by step avoids these errors.

Final Answer:
The expression 614 percent of 1600 plus 1212 percent of 800 evaluates to 19520.