Profit and Loss Calculation in Sales: An Analysis of Two TV Sets

Introduction

The concept of profit and loss is a critical aspect of business and economics. Often, businesses or individuals might sell items at a gain or loss, but it's not always clear if the overall transaction results in a profit or a loss. This article delves into an interesting problem involving the sale of two television sets to understand such scenarios.

The Problem

A man sold two TV sets for Rs. 9900 each. He gained 10% on one and lost 10% on the other. The question is: did he gain or lose on the whole, and if so, by how much?

Profit and Loss Calculation

To solve this, we need to calculate the cost price (CP) of each TV based on the selling price (SP) and the profit/loss percentages.

Calculation for the First TV Set

The selling price (SP) for the first TV set is Rs. 9900, and he gained 10% on it.

Formula:
SP CP_1 × (1 Gain Percentage)

Substituting the values:

9900 CP_1 × 1.10

CP_1 9900 / 1.10 Rs. 9000

Calculation for the Second TV Set

The selling price (SP) for the second TV set is also Rs. 9900, but this time, he lost 10% on it.

Formula:
SP CP_2 × (1 - Loss Percentage)

Substituting the values:

9900 CP_2 × 0.90

CP_2 9900 / 0.90 Rs. 11000

Total Cost Price and Selling Price

Total cost price (CPtotal) of both TV sets:

CPtotal CP_1 CP_2 9000 11000 Rs. 20000

Total selling price (SPtotal) of both TV sets:

SPtotal 9900 9900 Rs. 19800

Gain or Loss Calculation

Total gain or loss:

Total Loss SPtotal - CPtotal 19800 - 20000 -Rs. 200

Since the result is negative, it indicates a loss of Rs. 200.

An Alternative Approach

Another simpler method involves understanding that a 10% loss on a cost price of 100 gives a selling price of 90, while a 10% profit on a cost price of 100 gives a selling price of 110. When these are added together, the total selling price becomes 200, and the total cost price remains 200 as well.

However, in this scenario, since one TV was sold at a profit and the other at a loss, there is a net loss.

Conclusion

In the first scenario, the man incurred a loss of Rs. 200 from the sale of the two TV sets.

Market Rate Calculation

The market rate for a typical TV set can be calculated as follows:

Market Rate of first TV set:

37000 / 110 Rs. 3363.63

Market Rate of second TV set:

3700 / 0.9 Rs. 4111.11

Total market rate:

3363.63 4111.11 Rs. 7474.74

Selling rate:

Rs. 7400

Total cost:

Rs. 7474.75

Loss:

Rs. 74.75

Loss percentage:

(74.75 / 7474.75) × 100 1%

Additional Examples

In another scenario, a dealer sold two TV sets for Taka 3700 each. He gained 10% on one and lost 10% on the other.

First TV Set Calculation

First TV set: SP 3700 and gain of 10%

Cost price (CP) of the first TV set:

CP 3700 / 1.1 3363.63 (rounded up)

Profit: 3700 - 3363.63 336.37

Second TV Set Calculation

Second TV set: SP 3700 and loss of 10%

Cost price (CP) of the second TV set:

CP 3700 × 0.9 3330

Loss: 3700 - 3330 370

Total Profit/Loss Calculation

Total cost:

3363.63 3330 6693.63

Total selling price:

3700 3700 7400

Total loss:

7400 - 6693.63 706.37

Percentage loss:

(706.37 / 6693.63) × 100 ≈ 10.57% (rounded up)

The calculations demonstrate that in both scenarios, there is a net loss despite selling each item for the same price due to the different profit and loss percentages.