Targeting a different outcome price: Raj sells an item for ₹ 6,384 at a 30% loss. At what price should he have sold the same item to make a 30% profit?

Introduction / Context:
Switching from a loss to a profit on the same article requires first recovering the cost price from one scenario and then applying the desired percentage to get the new selling price.

Given Data / Assumptions:

• SP_loss = ₹ 6,384 at 30% loss.
• Desired profit = 30% on the same cost price.

Concept / Approach:
If loss is 30%, SP = 0.70 * CP ⇒ CP = SP / 0.70. For a 30% profit, SP_target = 1.30 * CP.

Step-by-Step Solution:
CP = 6,384 / 0.70 = ₹ 9,120SP_target = 1.30 * 9,120 = ₹ 11,856

Verification / Alternative check:
Check consistency: 30% of 9,120 is 2,736; 9,120 + 2,736 = 11,856, confirming the result.

Why Other Options Are Wrong:

• ₹ 13,544 / ₹ 14,656: incorrect multipliers or arithmetic.
• Cannot be determined: CP is exactly recoverable from the given loss scenario.

Common Pitfalls:

• Averaging 30% loss and 30% profit as if symmetric in price; the base changes (cost vs. selling price).

Final Answer:
₹ 11,856