Arun's Computer Puzzle Unraveling The Math Mystery

Hey guys! Ever stumbled upon a math problem that feels like a detective novel? Well, I've got one for you today. It involves Arun, an old computer, some repairs, and a series of sales with profits and losses. Sounds intriguing, right? Let's dive into this mathematical mystery and unravel it step-by-step.

The Puzzle: Tracing the Computer's Journey

Arun started this whole adventure by buying an old computer. Now, the crucial piece we're missing is the original price Arun paid – that's our ultimate goal to find. But the story doesn't end there! Arun, being the savvy person he is, spent ₹110 on repairing the computer to get it back in tip-top shape. This is the beginning cost we need to consider. Afterwards, he sold it to Bhola, making a sweet 20% profit on the deal. Bhola then sold the computer to Chandan, but unfortunately, Bhola faced a 10% loss in this transaction. Finally, Chandan sold the computer for ₹1188, earning a 10% profit. The question staring us in the face is: What was the price Arun originally paid for the old computer?

Unraveling the Mystery: A Step-by-Step Solution

To solve this, we'll work backward, tracing the computer's journey from the final selling price back to Arun's initial purchase. This is where the real fun begins, guys!

Chandan's Perspective: The Final Sale

• Starting Point: Chandan sold the computer for ₹1188, making a 10% profit. This is our last known point, we will start backwards from here.
• Decoding the Profit: This means ₹1188 represents 110% of the price Chandan paid (100% of the cost + 10% profit). It's like saying Chandan's selling price is a boosted version of what he bought it for.
• Finding Chandan's Cost Price: To find out how much Chandan paid, we can set up a simple equation:
  • Let Chandan's cost price be 'C'.
  • 1. 10 * C = ₹1188 (Since ₹1188 is 110% of C)
  • C = ₹1188 / 1.10 = ₹1080
• The Revelation: So, Chandan bought the computer for ₹1080. We are moving backwards, this is an important finding!

Bhola's Transaction: The Loss Encounter

• Bhola's Predicament: Bhola sold the computer to Chandan at a 10% loss. This means Chandan's purchase price (₹1080) represents 90% of what Bhola paid (100% - 10% loss).
• Unmasking Bhola's Cost Price: Again, let's use an equation to figure out Bhola's cost price:
  • Let Bhola's cost price be 'B'.
  • 0. 90 * B = ₹1080 (Since ₹1080 is 90% of B)
  • B = ₹1080 / 0.90 = ₹1200
• The Discovery: Bhola, therefore, bought the computer for ₹1200. We are closer to the beginning, guys!

Arun's Sale: The Profit Margin

• Arun's Triumph: Arun sold the computer to Bhola at a 20% profit. This means Bhola's purchase price (₹1200) is 120% of the price Arun had after the repairs (100% of the cost + 20% profit).
• Calculating Arun's Price After Repairs: Let's keep the equation train rolling to find out Arun's price after the repairs:
  • Let Arun's price after repairs be 'A'.
  • 20 * A = ₹1200 (Since ₹1200 is 120% of A)
  • A = ₹1200 / 1.20 = ₹1000
• The Breakthrough: Arun's price after repairing the computer was ₹1000. The picture is getting clearer, isn't it?

The Final Piece: Arun's Original Investment

• The Repair Factor: Remember, Arun spent ₹110 on repairs. This amount was added to his original purchase price.
• Revealing Arun's Initial Cost: To find the original cost, we simply subtract the repair cost from the price after repairs:
  • Arun's original cost = ₹1000 (price after repairs) - ₹110 (repair cost) = ₹890
• The Grand Finale: Therefore, Arun originally bought the old computer for ₹890! We cracked it, guys!

Key Takeaways: Strategies for Solving Similar Problems

This problem, while seemingly complex, becomes manageable when broken down into smaller steps. Here are some key takeaways and strategies that will help you solve similar mathematical mysteries in the future:

Working Backwards: A Powerful Technique

The most effective strategy in this scenario was working backward from the final selling price. When faced with a series of transactions or changes, starting from the end and working your way back to the beginning can simplify the problem significantly. This approach allows you to unravel the layers of transactions one at a time, making it easier to isolate the unknown variable. In this case, by starting with Chandan's sale and moving back through Bhola's transaction to Arun's initial purchase, we were able to methodically determine the original price of the computer. This method is particularly useful when the initial value is obscured by subsequent operations.

Percentage Calculations: The Core Skill

Understanding percentage calculations is absolutely crucial for solving problems involving profits, losses, and discounts. Each percentage represents a portion of a whole, and being able to convert percentages to decimals (and vice versa) is essential for accurate calculations. In this problem, we had to calculate both profits (percentage increase) and losses (percentage decrease) at different stages of the computer's journey. Knowing how to express these changes mathematically – for example, understanding that a 20% profit means multiplying the cost price by 1.20 – is key to solving these types of problems efficiently. Mastering these calculations will not only help in mathematical problem-solving but also in real-life financial scenarios.

Setting Up Equations: A Systematic Approach

Formulating equations is a powerful method for organizing and solving mathematical problems. By assigning variables to unknown quantities and representing the relationships between them mathematically, you can create a clear framework for finding solutions. In this problem, we used equations to represent the cost price at each stage of the transaction. For instance, we expressed Chandan's cost price as 'C' and then created an equation to relate it to the selling price. This systematic approach not only simplifies the calculations but also reduces the chances of making errors. Learning to translate word problems into mathematical equations is a valuable skill that can be applied to a wide range of problems.

Breaking Down Complexity: The Art of Simplification

Complex problems often seem daunting at first glance, but they can become much more manageable when broken down into smaller, more digestible parts. In this case, we divided the problem into individual transactions – Chandan's sale, Bhola's transaction, and Arun's sale – and solved each one separately. This divide-and-conquer approach allowed us to focus on one aspect of the problem at a time, making the overall solution process less overwhelming. By identifying the key information in each transaction and addressing it step-by-step, we were able to gradually uncover the answer. This strategy is applicable not just to math problems, but to any complex task or project.

Double-Checking Your Work: Ensuring Accuracy

Finally, it's always a good idea to double-check your work to ensure accuracy. After solving the problem, take a moment to review each step and verify that the calculations are correct and the logic is sound. This is especially important in multi-step problems where an error in one step can propagate through the rest of the solution. In our computer problem, you could check your answer by starting with Arun's purchase price and working forward through the transactions to see if you arrive at Chandan's final selling price. This practice not only helps you catch mistakes but also reinforces your understanding of the problem and the solution process. Accuracy is paramount, especially in math and finance-related tasks.

Real-World Applications: Where Math Meets Life

The problem we just solved isn't just a theoretical exercise; it has real-world applications. Understanding profit and loss calculations is essential in various aspects of life, from personal finance to business management. Here are a few examples:

• Business: Businesses use profit and loss calculations to determine the profitability of their products or services. They need to know their cost price, selling price, and expenses to calculate their profit margins. This information is crucial for making informed decisions about pricing, production, and inventory management.
• Investing: Investors use profit and loss calculations to assess the performance of their investments. They need to know the purchase price of an asset (such as stocks or bonds), the selling price, and any associated costs to determine their return on investment. Understanding these calculations helps investors make informed decisions about buying and selling assets.
• Personal Finance: Individuals can use profit and loss calculations to make informed decisions about their personal finances. For example, when buying or selling a car, calculating the profit or loss can help you determine whether you got a good deal. Similarly, understanding these calculations can help you manage your household budget and make informed purchasing decisions.
• Retail: Retailers use profit and loss calculations to set prices and determine discounts. They need to balance their desire to make a profit with the need to attract customers and clear inventory. Understanding these calculations helps retailers make strategic pricing decisions that maximize their profitability.
• Real Estate: Real estate investors use profit and loss calculations to evaluate potential property investments. They need to consider the purchase price, renovation costs, rental income, and selling price to determine the potential return on investment. These calculations help investors identify profitable real estate opportunities.

Conclusion: Math is an Adventure!

So, there you have it, guys! We've successfully navigated the twists and turns of Arun's computer sale and discovered the original price he paid. Math problems like these might seem intimidating at first, but with a systematic approach and a bit of logical thinking, they can be quite fun to solve. Remember, the key is to break down the problem, understand the concepts, and double-check your work. Keep practicing, and you'll become a math detective in no time!

Math isn't just about numbers and equations; it's about problem-solving, critical thinking, and understanding the world around us. By honing our mathematical skills, we can make better decisions, analyze information more effectively, and tackle challenges with confidence. So, keep exploring, keep questioning, and keep the mathematical adventure going!