Determining the Cost Price of Books: A Comprehensive Guide

This article will guide you through a detailed step-by-step process to determine the cost price of books sold at different profit percentages. We will use an example problem to illustrate the methodology, and explain how to solve similar problems effectively.

Problem Statement

A bookseller sold 60 books at a 5% profit and 80 books at a 15% profit. If he had sold all books at a 20% profit, he would have earned a total profit of Rs. 1560. The task is to find the cost price of one book.

Step-by-Step Solution

Step 1: Calculate the Profit from the Books Sold

Let C represent the cost price of one book. We need to compute the profit for each set of books sold at different profit percentages.

For 60 books sold at 5% profit:

[text{Profit}_{60} 60 times C times frac{5}{100} 3C]

For 80 books sold at 15% profit:

[text{Profit}_{80} 80 times C times frac{15}{100} 12C]

Total Profit from the Two Sets of Books

Add the profits from both sets of books:

[text{Total Profit} text{Profit}_{60} text{Profit}_{80} 3C 12C 15C]

Step 2: Profit if All Books Were Sold at 20% Profit

The total profit for selling all 140 books at 20% profit is:

[text{Profit}_{20} 140 times C times frac{20}{100} 28C]

Step 3: Equation from the Given Information

According to the problem, this profit (28C) is equal to Rs. 1560:

[28C 1560]

Step 4: Solve for C

To find the cost price:

[C frac{1560}{28} 55.71428571428571 approx 55.71]

Thus, the cost price of one book is approximately 55.71.

Alternative Method: Shortcut Approach

Let's consider a simpler method to solve this problem just to illustrate alternative ways:

Step 1: Total books 60 80 140.

Step 2: Profit difference calculation,

From problem 20 - 15 5, 1560/Rs 13*120, so each book 120, cost price.

Conclusion

The cost price of one book is approximately 55.71. Using this cost price, we can verify the total cost and sales values to ensure our calculations are correct.

Additional Tips

When solving such problems, always define a variable for the cost price, and then systematically calculate the profit from each set of books sold. Use clear steps and verify your results using multiple approaches to ensure accuracy.

Remember, consistency and clear steps are key to solving and understanding similar profit and cost problems.