Introduction

This article delves into a complex mathematical scenario involving successive sales transactions, where the buyer incurs losses or profits at various stages. We will utilize algebraic expressions and arithmetic operations to calculate the cost price, selling price, and economic losses incurred by different parties in the transactions. This analysis is not only relevant to economic studies but also provides valuable insights into the complexities of market transactions and pricing strategies.

Problem Statement

A sold an article to B at a loss of 20%. B then sold the article to C at a profit of 12.5%. Finally, C sold the article to D at a 8% loss. If D paid Rs 48.4 for the article, determine the difference in the loss incurred by A and C.

Step-by-Step Analysis

1. Identifying the Cost Price for A

We denote the cost price of the article for A as CP_A.

2. Transaction from A to B

A sells the article to B at a loss of 20%, which means:

SP_B CP_A × (1 - 0.20) 0.80 × CP_A

3. Transaction from B to C

B then sells the article to C at a profit of 12.5%, which means:

SP_C SP_B × (1 0.125) 0.80 × CP_A × 1.125 0.90 × CP_A

4. Transaction from C to D

C sells the article to D at a 8% loss, which means:

SP_D SP_C × (1 - 0.08) 0.90 × CP_A × 0.92 0.828 × CP_A

5. Given Information and Calculation

We are given that D pays Rs 48.4 for the article, so we can write the equation:

0.828 × CP_A 48.4

Therefore, CP_A can be calculated as:

CP_A 48.4 / 0.828 ≈ 58.5

Calculating Loss Incurred by A and C

6. Loss Incurred by A

The selling price for A is SP_B, which means:

SP_B 0.80 × CP_A 0.80 × 58.5 46.8

The loss incurred by A is:

Loss by A CP_A - SP_B 58.5 - 46.8 11.7

7. Loss Incurred by C

The selling price for C is SP_D, which means:

SP_D 0.828 × CP_A 0.828 × 58.5 48.4

The loss incurred by C is:

Loss by C SP_C - SP_D 0.90 × CP_A - 48.4 0.90 × 58.5 - 48.4 52.65 - 48.4 4.25

8. Difference in Losses

The difference in the loss incurred by A and C is:

Difference Loss by A - Loss by C 11.7 - 4.25 7.45

Therefore, the difference in the loss incurred by A and C is approximately 7.45 (Rs).

Conclusion

By carefully analyzing the given transactions, we can conclude that the difference in the loss incurred by A and C is approximately 7.45 Rs. This detailed analysis not only helps in evaluating the economic outcomes of each transaction but also provides insights into the significance of market fluctuations and pricing strategies.