Question

\(60 \%\) goods are sold at \(5 \%\) loss while rest are sold at \(10 \%\) profit. If there is a total profit of Rs. 100 , then the worth of goods sold is: (a) Rs. 6000 (b) Rs. 5000 (c) Rs. 10000 (d) none of these

Short answer

Answer: (c) Rs. 10000.

Step-by-step solution

Define the variables

Let's define the variables for our calculation. Let the total worth of goods sold be denoted by `W`. Let `x` represent the worth of goods sold at a loss, and `y` represent the worth of goods sold at a profit.

Calculate the Loss and Profit

Using the given percentage values, calculate the loss and profit for each category. Loss on goods sold at \(5 \%\) = \(0.05x\) Profit on goods sold at \(10 \%\) = \(0.10y\)

Write the equations

We are given that \(60 \%\) of the goods are sold at a loss and the remaining are sold at a profit. So, we can write the following equations to represent these conditions. \(x = 0.6W\) \(y = 0.4W\) It is also given that the net profit is Rs. 100. We can write the equation for the total profit as follows: \(0.10y - 0.05x = 100\)

Solve the equations

Now, we have two equations with two variables (x and y). We can use them to find the total worth of goods sold (W). Substitute the values of x and y from the first two equations into the third equation: \(0.10(0.4W) - 0.05(0.6W) = 100\) Simplify the equation: \(0.04W - 0.03W = 100\) Combine like terms: \(0.01W = 100\) Now, divide both sides by 0.01 to solve for W: \(W = 100/0.01\)

Calculate the total worth of goods sold and select the answer

Solve for W: \(W = 10000\) So, the total worth of goods sold is Rs. 10000. The correct answer is (c) Rs. 10000.

Key concepts

Quantitative Aptitude

Quantitative aptitude is a critical facet of competitive exams and it involves the ability to reason logically with numbers and other mathematical concepts. It encompasses a wide range of topics, including profit and loss, which is an essential part of business mathematics.

In the context of profit and loss problems, an understanding of quantitative aptitude enables you to analyze transactions, calculate percentages, and determine the outcomes of business dealings in monetary terms. It isn't just about applying formulas; it's about understanding the relationship between the cost price, selling price, and how these relate to the profits or losses made.

For instance, understanding how to weigh the impact of selling a particular percentage of goods at a loss versus a profit is crucial. This arithmetic skill does not only apply to traditional arithmetic problems but also to real-life scenarios where one must make decisions based on potential financial outcomes. The problem provided is a perfect example where quantitative aptitude is applied to dissect the scenario involving the sale of goods at varying profit and loss margins.

Percentage Profit and Loss

Understanding percentage profit and loss is crucial for students and professionals alike because it represents the relation of profit or loss to the cost price in terms of percent. In practical terms, this helps both businesses to project their financial health and individuals to manage their personal finance decisions.

To calculate the percentage profit, one would use the formula:
\[\begin{equation}Percentage Profit = \frac{{Profit}}{{Cost Price}} \times 100\%\end{equation}\]
And similarly, to calculate percentage loss:
\[\begin{equation}Percentage Loss = \frac{{Loss}}{{Cost Price}} \times 100\%\end{equation}\]
In the given exercise, recognizing the percentage of goods sold at a profit or a loss, and calculating their respective impacts further enhances one's ability to perform successful problem-solving. The practical application of these concepts teaches us about trade-offs and decision-making in business contexts, as it relates to pricing strategies and inventory management.

Linking to Real-world Scenarios

Percentage profit and loss calculations are not only confined to textbook problems, but they are also deeply entrenched in everyday activities such as shopping discounts, stock market investments, and business revenue assessments. By mastering this concept, students can approach financial decisions with acumen and confidence.

Problem Solving in Mathematics

Problem solving in mathematics is more than just crunching numbers; it's a thought process that involves understanding the problem, planning an approach, and then executing the necessary steps to arrive at a solution. It is a skill that is nurtured over time through practice and application of various strategies and mathematical concepts.

In solving the textbook problem presented, the step-by-step solution starts with defining the variables and establishing relationships between them through equations. This systematic approach breaks down the complexity into manageable chunks and is essential for tackling intricate quantitative aptitude problems.

One effective problem-solving technique used in this scenario is working backward from the given information, which in this case is the total net profit, to determine the unknown values. Implementing such strategies not only provides a structured framework to solve the problem at hand but also equips one with the tools to tackle a myriad of mathematical challenges faced in academic and professional environments.

Transferring Skills Beyond Mathematics

Problem-solving skills acquired through mathematics are transferable to various areas, such as critical thinking in personal decision making or logical reasoning in technical fields. Developing these skills encourages a methodical approach to facing challenges, reinforcing the importance of logic and persistence.