Calculating Rita's Final NOA Payout Points After A 10% Reduction

Rita initially has 45 NOA payout points. Due to invalid accounts, the bank reduces her NOA payout points by 10%. We need to calculate her final NOA payout points after this reduction. The provided options are:

(A) 36 (B) 40.5 (C) 41 (D) 45

Understanding the Problem

This is a percentage decrease problem. Percentage decrease problems are a common type of mathematical problem encountered in various real-life scenarios, from calculating discounts on purchases to understanding financial losses. In this specific scenario, we are tasked with determining the impact of a 10% reduction on Rita's initial NOA (No Objection Account) payout points. To solve this effectively, it's essential to first grasp the fundamental concept of percentages and how they relate to the whole. A percentage is essentially a way of expressing a number as a fraction of 100. Therefore, 10% can be interpreted as 10 out of every 100, or simply 10/100. This fraction can be further simplified to 1/10, making it easier to work with in calculations. When dealing with percentage decreases, the core principle involves calculating the amount of the decrease and then subtracting it from the original value. In our case, this means we need to find 10% of Rita's initial payout points and then subtract that value from her original total. Before diving into the calculations, it's crucial to clearly understand the initial conditions. Rita starts with 45 NOA payout points, which represents her total or original value. The 10% reduction acts as the variable that will affect this original value. Once we've determined the amount of the reduction, we can subtract it from the initial payout points to arrive at Rita's final payout points. This meticulous approach to understanding the problem and breaking it down into smaller, manageable steps is key to solving percentage decrease problems accurately. By focusing on the core concepts and carefully applying them to the specific details of the problem, we can confidently arrive at the correct solution.

Calculating the Reduction

The first step in solving this problem is to calculate the amount by which Rita's NOA payout points are reduced. The problem states that the reduction is 10% of her initial 45 points. To find 10% of 45, we can multiply 45 by 10% (or 0.10). This can be written as:

Reduction = 10% of 45 = 0.10 * 45

Performing this multiplication gives us:

Reduction = 4.5

This means that Rita's NOA payout points are reduced by 4.5 points. Understanding this calculation is crucial as it forms the basis for determining her final payout points. The concept of finding a percentage of a number is a fundamental skill in mathematics with broad applications in everyday life. For instance, it is used in calculating discounts while shopping, figuring out interest on loans or investments, and determining taxes. In this specific scenario, we apply this skill to calculate the reduction in Rita's NOA payout points. The key is to convert the percentage into a decimal or a fraction before performing the multiplication. As we've seen, 10% is equivalent to 0.10 in decimal form. Multiplying 0.10 by the original number gives us the value of the reduction. In the context of this problem, the reduction of 4.5 points represents the impact of the invalid accounts on Rita's payout points. This value is the amount that will be subtracted from her initial payout points to determine her final total. By accurately calculating the reduction, we set the stage for the final step in the problem-solving process, which involves subtracting the reduction from the original value. This step will provide us with the definitive answer to the question of Rita's final NOA payout points.

Calculating Final Payout Points

Now that we know the reduction is 4.5 points, we can calculate Rita's final NOA payout points. This is done by subtracting the reduction from her initial points:

Final Points = Initial Points - Reduction

Substituting the values we have:

Final Points = 45 - 4.5

Performing the subtraction gives us:

Final Points = 40.5

Therefore, Rita's final NOA payout points after the 10% reduction are 40.5. This final calculation is a crucial step in determining the answer to the problem, as it directly addresses the question posed: what will be her final NOA payout points? The process of subtracting the reduction from the initial value is a fundamental arithmetic operation that is used extensively in various mathematical and real-world contexts. It allows us to determine the remaining quantity after a certain amount has been removed or decreased. In this particular scenario, subtracting the reduction of 4.5 points from Rita's initial 45 points gives us the final payout points she will have after the deduction due to invalid accounts. The result of 40.5 points represents Rita's new total after the 10% reduction has been applied. It is important to note that this value is less than her initial payout points, which is consistent with the concept of a percentage decrease. The final payout points of 40.5 directly address the core objective of the problem, providing a clear and concise answer to the question at hand. This value can then be compared to the options provided in the problem statement to identify the correct choice. By carefully performing the subtraction and arriving at the final payout points, we complete the problem-solving process and arrive at the solution.

Selecting the Correct Option

Comparing our calculated final payout points (40.5) with the given options:

(A) 36 (B) 40.5 (C) 41 (D) 45

We can see that option (B) 40.5 matches our calculated value. Thus, the correct answer is (B). Selecting the correct option is the final step in the problem-solving process, where we match our calculated result with the available choices to identify the most accurate answer. This step requires careful comparison and attention to detail to ensure that we select the option that aligns perfectly with our calculations. In this case, after determining that Rita's final NOA payout points are 40.5, we meticulously examine the given options to find the one that corresponds to this value. By comparing our calculated result (40.5) with each of the options, we can confidently identify option (B) as the correct answer. This step highlights the importance of not only performing the calculations accurately but also verifying the results by comparing them with the available options. It ensures that we have not made any errors in our calculations and that we are selecting the most appropriate answer. The final selection of the correct option signifies the successful completion of the problem-solving process, where we have not only understood the problem but also applied the necessary mathematical concepts and calculations to arrive at the accurate solution. This process reinforces the importance of a systematic approach to problem-solving, where each step is carefully executed and verified to ensure the overall correctness of the final answer.

Final Answer

The correct answer is (B) 40.5.

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