Two-article sale: one sold at 10% loss and the other at 15% profit. Overall there is no profit or loss. If the combined selling price is Rs 30,000, find the difference between their cost prices.

Introduction:
When the net result is break-even, total SP equals total CP. Combine this with individual percentage relations to relate the two cost prices and then use the total SP to solve.

Given Data / Assumptions:

• Article 1: 10% loss ⇒ SP1 = 0.9 * CP1.
• Article 2: 15% profit ⇒ SP2 = 1.15 * CP2.
• Overall: SP1 + SP2 = CP1 + CP2 and SP1 + SP2 = Rs 30,000.

Concept / Approach:
From break-even: 0.9CP1 + 1.15CP2 = CP1 + CP2 ⇒ 0.1CP1 = 0.15CP2 ⇒ CP1 = 1.5CP2. Then use SP total to solve CP2.

Step-by-Step Solution:
CP1 = 1.5 CP2Total SP = 0.9(1.5CP2) + 1.15CP2 = 1.35CP2 + 1.15CP2 = 2.5CP2 = 30,000CP2 = 12,000 ⇒ CP1 = 18,000Difference = |18,000 − 12,000| = Rs 6,000

Verification / Alternative check:
SP1 = 16,200; SP2 = 13,800; sum = 30,000 equals CP1 + CP2 = 30,000, confirming break-even and the difference.

Why Other Options Are Wrong:

• Rs 5,000 / Rs 7,500: arise from algebra mistakes in the ratio step.
• None of these: incorrect because Rs 6,000 is exact.

Common Pitfalls:

• Averaging percentages or ignoring that break-even ties totals, not individual items.

Final Answer:
Rs.6000