Profit and Loss — Selling an article at ₹ 64 results in a 20% loss. At what selling price would the trader get a 20% profit on the same article?

Introduction / Context:
Sequentially changing the selling price from a loss scenario to a profit scenario involves first recovering the cost price (CP), then applying the desired profit percentage on CP to compute the new selling price (SP).

Given Data / Assumptions:

• SP_loss = ₹ 64 corresponds to a 20% loss.
• Target: 20% profit on the same CP.

Concept / Approach:
With 20% loss, SP = 0.80 * CP ⇒ CP = SP / 0.80. With 20% profit, SP_new = 1.20 * CP. Chain these to find the required SP.

Step-by-Step Solution:

Verification / Alternative check:
On CP = 80, SP = 96 yields profit% = (96 − 80)/80 * 100 = 20% (as required).

Why Other Options Are Wrong:
98, 94, 99, and 92 correspond to profit percentages different from 20% when CP = 80.

Common Pitfalls:
Adding 40 to ₹ 64 directly (treating 20% of 64), which is incorrect since the percentage must be applied to CP, not to the previous SP.

Final Answer:
Rs. 96