Points to Remember:
- This is a mathematical word problem involving profit and loss percentages.
- We need to set up equations based on the given information to solve for the cost price of the cycle.
- The solution will involve understanding the relationship between cost price, selling price, profit, and loss.
Introduction:
Profit and loss are fundamental concepts in business and economics. Profit is the gain made on a transaction, while loss is the amount by which the cost exceeds the selling price. These are usually expressed as percentages relative to the cost price. This problem requires us to use the given information about percentage loss and percentage profit to determine the original cost price of the cycle.
Body:
1. Defining Variables and Setting up Equations:
Let’s denote:
- CP = Cost Price of the cycle (what we need to find)
- SP = Selling Price of the cycle
We are given that the trader sold the cycle at a 10% loss. This can be expressed as:
SP = CP – 0.10CP = 0.90CP (Equation 1)
If the selling price had been increased by â¹200, there would have been a 6% profit. This can be expressed as:
SP + 200 = CP + 0.06CP = 1.06CP (Equation 2)
2. Solving the Equations:
We now have a system of two equations with two variables. We can substitute Equation 1 into Equation 2:
0.90CP + 200 = 1.06CP
Subtracting 0.90CP from both sides:
200 = 1.06CP – 0.90CP
200 = 0.16CP
Dividing both sides by 0.16:
CP = 200 / 0.16 = â¹1250
3. Verification:
Let’s verify our answer.
- Cost Price (CP): â¹1250
- Selling Price (SP) at 10% loss: 1250 * 0.90 = â¹1125
- Selling Price (SP) with â¹200 increase: 1125 + 200 = â¹1325
- Profit at the increased SP: (1325 – 1250) / 1250 = 0.06 = 6%
The calculations confirm our solution.
Conclusion:
The cost price of the cycle is â¹1250. This problem demonstrates the practical application of percentage calculations in business transactions. By carefully setting up and solving equations based on the given information, we can accurately determine unknown variables. Understanding profit and loss calculations is crucial for sound financial management in any business, ensuring sustainable growth and profitability. This approach highlights the importance of clear mathematical reasoning in solving real-world problems.