Calculating the Cost Price of a Book Given Profit Percentages

In this article, we will solve a common yet intriguing math problem involving the cost price and sales profit. Specifically, we will calculate the cost price of a book when a boy purchased both a book and a pen for 100 and sold them with different profit margins.

Solving the Problem Using Algebraic Equations

Let's denote the cost price of the pen as P, and the cost price of the book as B. Given that the total cost price of the book and the pen is 100, we can write the equation:

B P 100

The boy then sold the pen at a profit of 20%, which implies the selling price of the pen is 1.20 times the cost price. Similarly, the book was sold at a profit of 25%, which means the selling price of the book is 1.25 times the cost price. The combined profit from selling both the pen and the book is 22, which leads to the following equation:

0.20P 0.25B 22

Step-by-step Solution

Now, let's solve the system of equations step by step.

First, from the total cost price equation:

P 100 - B

Substitute this into the combined profit equation to get:0.20(100 - B) 0.25B 22

Expanding and simplifying the equation:20 - 0.20B 0.25B 22

Combining like terms:0.05B 2

Dividing both sides by 0.05:B 40

Conclusion

Therefore, the cost price of the book is Rs. 40.

Additional Insights and Applications

This type of problemolving technique is not only useful in academic settings but also in real-life situations where profit and cost calculations are needed. Whether you're a business owner, an investor, or a student, understanding how to calculate profit margins and cost prices is invaluable.

By breaking down the problem into simpler steps and using algebraic equations, we can tackle complex scenarios with ease. This method can also be applied to various other business problems such as discount calculations, revenue forecasting, and more.

Conclusion

Calculating the cost price of a book, given the total cost and profit percentages, is a straightforward yet insightful exercise in algebra. Understanding how to approach such problems can enhance your analytical skills and provide practical solutions in various contexts.

Key Takeaways

Use algebraic equations to solve cost price and profit calculation problems. Break down the problem into simpler parts to make it easier to solve. Apply this method to other real-world business scenarios for effective problem-solving.

References and Further Reading

For further study on cost price and profit calculations, you may refer to standard textbooks on economics, business mathematics, or online resources such as Khan Academy.