Ram Purchases A Bicycle For RS 140,000, Including A $13 %$ VAT. He Makes A $30 %$ Profit On The Bicycle. Find The Selling Price Of The Bicycle.
Introduction
In this article, we will delve into a mathematical problem involving a bicycle purchase and profit calculation. Ram, a keen cyclist, buys a bicycle for a total amount of Rs 140,000, which includes a Value-Added Tax (VAT) of 13%. He then makes a 30% profit on the bicycle. Our objective is to determine the selling price of the bicycle after Ram's profit margin is applied.
Calculating the Original Price of the Bicycle
To find the original price of the bicycle before the VAT is added, we need to subtract the VAT amount from the total purchase price. The VAT amount is 13% of the original price, which can be represented as 0.13x, where x is the original price.
Let's denote the original price of the bicycle as x. Then, the total purchase price, including VAT, is given by:
Total Purchase Price = Original Price + VAT = x + 0.13x = 1.13x
We are given that the total purchase price is Rs 140,000. Therefore, we can set up the equation:
1.13x = 140,000
To solve for x, we can divide both sides of the equation by 1.13:
x = 140,000 / 1.13 = 123,952.19
So, the original price of the bicycle is approximately Rs 123,952.19.
Calculating the Selling Price with a 30% Profit
Now that we have the original price of the bicycle, we can calculate the selling price after a 30% profit is applied. The profit amount is 30% of the original price, which can be represented as 0.30x.
The selling price is the sum of the original price and the profit amount:
Selling Price = Original Price + Profit = x + 0.30x = 1.30x
Substituting the value of x, we get:
Selling Price = 1.30(123,952.19) = 160,841.85
Therefore, the selling price of the bicycle after a 30% profit is approximately Rs 160,841.85.
Conclusion
In this article, we have calculated the selling price of a bicycle after a 30% profit is applied. We first determined the original price of the bicycle by subtracting the VAT amount from the total purchase price. Then, we applied a 30% profit to the original price to find the selling price. The result shows that the selling price of the bicycle is approximately Rs 160,841.85.
Key Takeaways
- The original price of the bicycle is approximately Rs 123,952.19.
- The selling price of the bicycle after a 30% profit is approximately Rs 160,841.85.
- To calculate the selling price, we need to apply a 30% profit to the original price.
Mathematical Formulas Used
- Total Purchase Price = Original Price + VAT
- Selling Price = Original Price + Profit
- Profit Amount = 0.30x
- Selling Price = 1.30x
Real-World Applications
This problem has real-world applications in various fields, such as:
- Business: Calculating the selling price of a product after a profit margin is applied.
- Finance: Determining the cost of a product or service after taxes and fees are applied.
- Economics: Analyzing the impact of taxes and profit margins on the price of a product.
Future Research Directions
- Investigating the impact of different profit margins on the selling price of a product.
- Analyzing the effect of taxes and fees on the price of a product.
- Developing mathematical models to predict the selling price of a product based on various factors.
Ram's Bicycle Purchase: A Mathematical Enquiry - Q&A =====================================================
Introduction
In our previous article, we explored the mathematical problem of Ram purchasing a bicycle for Rs 140,000, including a 13% VAT, and then making a 30% profit on the bicycle. We calculated the selling price of the bicycle after the profit margin was applied. In this article, we will address some frequently asked questions related to this problem.
Q&A
Q: What is the original price of the bicycle before the VAT is added?
A: The original price of the bicycle is approximately Rs 123,952.19.
Q: How do you calculate the selling price of the bicycle after a 30% profit is applied?
A: To calculate the selling price, you need to apply a 30% profit to the original price. The selling price is given by the formula: Selling Price = 1.30x, where x is the original price.
Q: What is the selling price of the bicycle after a 30% profit is applied?
A: The selling price of the bicycle after a 30% profit is approximately Rs 160,841.85.
Q: How does the VAT affect the total purchase price of the bicycle?
A: The VAT is 13% of the original price, which is added to the original price to get the total purchase price. The total purchase price is given by the formula: Total Purchase Price = 1.13x, where x is the original price.
Q: What is the impact of the profit margin on the selling price of the bicycle?
A: The profit margin of 30% increases the selling price of the bicycle by 30% of the original price. This means that the selling price is 130% of the original price.
Q: Can you provide a step-by-step solution to the problem?
A: Here is a step-by-step solution to the problem:
- Calculate the original price of the bicycle by subtracting the VAT amount from the total purchase price: x = 140,000 / 1.13
- Calculate the profit amount by multiplying the original price by the profit margin: Profit Amount = 0.30x
- Calculate the selling price by adding the profit amount to the original price: Selling Price = 1.30x
Q: What are some real-world applications of this problem?
A: This problem has real-world applications in various fields, such as:
- Business: Calculating the selling price of a product after a profit margin is applied.
- Finance: Determining the cost of a product or service after taxes and fees are applied.
- Economics: Analyzing the impact of taxes and profit margins on the price of a product.
Q: Can you provide some tips for solving similar problems?
A: Here are some tips for solving similar problems:
- Always read the problem carefully and understand what is being asked.
- Break down the problem into smaller, manageable parts.
- Use mathematical formulas and equations to represent the relationships between the variables.
- Check your work and make sure that your solution is reasonable and accurate.
Conclusion
In this article, we have addressed some frequently asked questions related to the problem of Ram purchasing a bicycle for Rs 140,000, including a 13% VAT, and then making a 30% profit on the bicycle. We have provided step-by-step solutions, real-world applications, and tips for solving similar problems. We hope that this article has been helpful in clarifying any doubts and providing a better understanding of the problem.