Solving Equations to Determine Actual Prices of Tea and Soup Sets

When dealing with financial puzzles and logical reasoning, the process of solving equations can unveil the actual prices of various items. Consider the scenario of a crockery seller who sells a tea set at a 5% loss and a soup set at a 15% gain, resulting in a gain of Rs. 7. In another case, if the tea sets are sold at a 5% gain and the soup sets at a 10% gain, the profit increases to Rs. 13. This article will walk you through the mathematical process to determine the original prices of the tea set and the soup set.

Setting Up the Equations

Let's denote the actual cost price of the tea set as Rs. X and the actual cost price of the soup set as Rs. Y. We need to set up a system of equations based on the given conditions.

First Case

According to the first condition, the selling price of the tea set at a 5% loss and the soup set at a 15% gain is such that the total gain is Rs. 7. The equations can be written as:

SP of tea set 0.95X and SP of soup set 1.15Y

Given SP - CP 7, we write:

0.95X 1.15Y - (X Y) 7

This simplifies to:

-0.05X 0.15Y 7 1

Second Case

In the second scenario, the tea set is sold at a 5% gain and the soup set at a 10% gain, with a resultant gain of Rs. 13:

SP of tea set 1.05X and SP of soup set 1.1Y

Given SP - CP 13, we write:

1.05X 1.1Y - (X Y) 13

This simplifies to:

0.05X 0.1Y 13 2

Combining the Equations

To solve for Y, we can add equations 1 and 2:

-0.05X 0.15Y 0.05X 0.1Y 7 13

0.25Y 20

Y 20 / 0.25 80

Thus, the actual cost price of the soup set (Y) is Rs. 80.

Solving for X

Now, substituting Y 80 into equation 1:

-0.05X 0.15 * 80 7

-0.05X 12 7

-0.05X -5

X 100

Thus, the actual cost price of the tea set (X) is Rs. 100.

Conclusion

The actual prices of the tea set and the soup set are Rs. 100 and Rs. 80, respectively. This solution clearly demonstrates the application of mathematical equations to solve real-world financial puzzles.

Keywords: mathematical equations, financial puzzles, logical reasoning