How to Solve a Profit and Cost Calculation Problem: A Step-by-Step Guide

Solving problems related to profit, cost, and selling price can sometimes be challenging, especially when the relationships between these variables are intertwined. In this post, we will delve into a specific example to illustrate how to solve such a problem effectively. We will use a practical example and provide a detailed step-by-step solution.

Problem Statement

An item was sold at a 6% profit. If the cost was 4 less and the selling price was TK. 4 more, the trader should have made a profit of 12.5%. What was the cost of the item?

Variables

Let the cost price of the item be C. Thus, the selling price when sold at a 6% profit is:

S C 0.06C 1.06C

Case 1: New Cost Price and Selling Price

If the cost price is 4 less, the new cost price becomes:

C' C - 0.04C 0.96C

According to the problem, the new selling price is TK. 4 more and the profit should be 12.5%. Therefore, the new selling price can be expressed as:

S' C' 0.125C' 1.125C'

Substituting C':

S' 1.125 × 0.96C 1.08C

Equating the Selling Prices

We now have two expressions for S:

S 1.06C

S' 1.08C

Substituting the first into the second:

1.06C 4 1.08C

Now, simplify this equation:

4 1.08C - 1.06C

4 0.02C

Solve for C:

C 4 / 0.02 200

Conclusion

Thus, the cost of the item is TK. 200.

Alternative Solutions

Here are a few alternative solutions that you can use to solve the same problem:

Solution 1: Enhanced Understanding of Ratios

- In 6% profit, the selling price 100 6 106 - 4 less the cost price 100 - 4 96 - At 12.5% profit, if CP is 100, then SP is 112.5 96 / 100 108 - The difference between SP 108 - 106 2 - 2 represents 100 in CP - 4/2 200

Solution 2: Simplifying the Calculation with Percentage Differences

- At 6% profit, the selling price 106 - At 4 less, the cost price 96 - At 12.5% profit, the selling price 96 96 × 12.5% 108 - The excess profit 108 - 106 2 - When earning 2 Tk more, the cost of the item is 100Tk 4 / 2 200Tk

Summary

In this post, we explored how to solve a problem involving profit, cost, and selling price, using a combination of algebraic manipulation and practical reasoning. By following a step-by-step approach, you can effectively tackle similar problems in the future.