Laptop And Mobile Phone: Profit & Loss Calculation

Hey everyone, let's dive into a fun math problem! This one is all about a laptop and a mobile phone, and figuring out whether a shopkeeper made a profit or took a loss on the whole deal. We're going to break it down step-by-step, so even if math isn't your favorite thing, you'll totally get it. This isn't just about crunching numbers; it's about understanding how businesses work and how profit and loss are calculated. So, grab a pen and paper, and let's get started! This problem is a classic example of how percentages and basic arithmetic are used in real-world scenarios. The concepts we'll cover are applicable to various financial situations, making it a valuable skill to have. We'll be looking at how to calculate the selling price of items when you know the cost price and the profit or loss percentage. We'll also be calculating the overall profit or loss percentage for the entire transaction. Understanding these concepts can help you make better financial decisions in your own life. Let's get to it!

Breaking Down the Costs: Laptop and Mobile Phone

First things first, let's look at the initial costs. The shopkeeper bought a laptop for ₹40,000 and a mobile phone for ₹24,000. These are our starting points – the cost prices (CP). Remember, the cost price is the amount the shopkeeper paid for the items. It's super important to have this number to calculate profit or loss. Now, why is knowing the cost price so important? It's the base from which we calculate profit or loss. If the selling price is higher than the cost price, we have a profit. If it's lower, we have a loss. The cost price sets the stage for the entire transaction. The total cost price is the sum of these two amounts, which sets up our understanding of the full expenditure. So, let's take a moment to appreciate these numbers as they lay the groundwork for our calculations. Let's clearly define what we're working with here. We've got the laptop's cost price and the mobile phone's cost price. These values are essential to understand how much profit or loss was made on each item.

To calculate the total cost price, we simply add the cost of the laptop and the cost of the mobile phone. The total cost price (Total CP) = ₹40,000 (Laptop) + ₹24,000 (Mobile) = ₹64,000. This is the total amount the shopkeeper spent to acquire both items. This is a key figure in determining the overall profit or loss. Think of it as the investment made. If the shopkeeper sells both items for more than ₹64,000, he makes a profit. If he sells them for less, he incurs a loss. Now that we've got the cost prices sorted, we can focus on the selling prices.

Calculating the Selling Price of the Laptop: Profit!

Alright, let's talk about the laptop. The shopkeeper made an 8% profit on the laptop. This means he sold the laptop for more than he bought it for. To find the selling price, we first need to calculate the profit amount. The profit on the laptop is 8% of ₹40,000. This is a straightforward percentage calculation. First, convert the percentage to a decimal by dividing by 100 (8 / 100 = 0.08). Then, multiply this decimal by the cost price of the laptop (0.08 * ₹40,000 = ₹3,200). So, the profit made on the laptop is ₹3,200. This profit is the reward for the shopkeeper’s business acumen! Knowing the profit is crucial because it tells us how much extra the shopkeeper earned from selling the laptop. Now, to find the selling price (SP) of the laptop, we add the profit to the cost price. This is the fundamental principle: selling price equals cost price plus profit. SP = CP + Profit. Therefore, the selling price of the laptop = ₹40,000 + ₹3,200 = ₹43,200. So, the shopkeeper sold the laptop for ₹43,200.

Why is the selling price so important? It is the actual amount of money the shopkeeper received from the sale. This is what goes into the shopkeeper’s pocket (before we consider the cost of the mobile phone). By knowing the selling price, we can now compare it with the cost price to determine the profit or loss. Let's take a moment to appreciate that we've calculated the profit and the selling price for the laptop. This sets the stage for the next calculation, where we will work on calculating the loss and selling price for the mobile phone. Now, we have successfully calculated the selling price, marking a significant step towards finding the overall profit or loss.

Calculating the Selling Price of the Mobile Phone: Loss!

Now, let's move on to the mobile phone. The shopkeeper had a 12% loss on the mobile phone. This means he sold the phone for less than he bought it for. First, let's calculate the loss amount. The loss on the mobile phone is 12% of ₹24,000. Convert 12% to a decimal (12 / 100 = 0.12). Then, multiply this decimal by the cost price (0.12 * ₹24,000 = ₹2,880). So, the loss on the mobile phone is ₹2,880. This loss is a setback for the shopkeeper; it’s important to know how this affects the overall outcome. This loss represents the amount by which the selling price will be less than the cost price. The loss is a decrease in the shopkeeper's earnings.

To find the selling price of the mobile phone, we subtract the loss from the cost price. In this case, the selling price is less than the cost price. SP = CP - Loss. Therefore, the selling price of the mobile phone = ₹24,000 - ₹2,880 = ₹21,120. So, the shopkeeper sold the mobile phone for ₹21,120.

Why is the selling price of the mobile phone important? It represents the actual amount of money the shopkeeper received from selling the mobile phone. With the selling price, we can now compare it with the cost price to determine the profit or loss. This is an important step towards determining the overall profit or loss. Let’s appreciate what we’ve done, we have calculated the loss and selling price for the mobile phone. This is essential information to calculate the overall profit or loss. Now, we can see that the selling price is less than the cost price, which reflects the loss. Now, we have successfully calculated the selling price of the mobile phone, a crucial step in determining the overall profit or loss.

Overall Profit or Loss: Putting It All Together

Alright, guys, now it's time to see the big picture! We need to find out if the shopkeeper made an overall profit or loss on the entire transaction. To do this, we first need to find the total selling price of both the laptop and the mobile phone. We already calculated the selling prices: Laptop = ₹43,200, Mobile Phone = ₹21,120. So, the total selling price (Total SP) = ₹43,200 + ₹21,120 = ₹64,320. This is the total amount of money the shopkeeper received from selling both items.

Next, we need to compare the total selling price with the total cost price. Remember, the total cost price was ₹64,000. We calculate the profit or loss by subtracting the total cost price from the total selling price. Profit/Loss = Total SP - Total CP. In this case, ₹64,320 - ₹64,000 = ₹320. Since the result is positive, it means the shopkeeper made a profit. This profit is the culmination of all the sales and purchases – the ultimate indicator of success! We can now determine if the overall transaction was a gain or a loss. The positive number shows us that the shopkeeper made a profit.

Why is the profit or loss so important? This is the bottom line. It’s what tells us whether the shopkeeper made money or lost money on the overall transaction. This is where we see the true financial performance of the entire transaction. Let's highlight the calculation we just did, the total selling price minus the total cost price, which helps us in determining the overall gain or loss.

Calculating the Overall Profit Percentage

To find the profit percentage on the whole transaction, we use this formula: Profit Percentage = (Profit / Total CP) * 100. We found a profit of ₹320, and the total CP was ₹64,000. Profit Percentage = (₹320 / ₹64,000) * 100 = 0.5%. This is the final step, the overall profit percentage summarizes the financial performance of the shopkeeper! This profit percentage is the actual return relative to the total cost. Let’s interpret the results, a 0.5% profit represents a successful transaction, showcasing the shopkeeper's business acumen. A profit percentage lets us know exactly how well the shopkeeper did when they bought and sold the items. Let's highlight the calculation of the overall profit percentage. We use the total profit and the total cost price, which reflects the profit in a relative context. This way we can clearly see the shopkeeper's overall performance.

Conclusion

So there you have it, guys! The shopkeeper made a profit of ₹320 on the whole transaction, which translates to a 0.5% profit. Even though there was a loss on the mobile phone, the profit from the laptop was enough to offset it and still make a small overall profit. This problem shows us how important it is to look at the entire picture, not just individual transactions, when figuring out profit and loss. Understanding these concepts helps you better manage your finances and make informed decisions, whether you're running a business or managing your own money.