Profit and Loss — A watch sold at ₹ 405 incurs a 10% loss (so CP = ₹ 450). If it is sold at ₹ 465 instead, determine the new gain or loss percentage.

Introduction / Context: Knowing one transaction’s loss lets us recover CP. With CP known, any alternative SP can be compared to CP to find the new profit or loss% quickly.

Given Data / Assumptions:

• SP_1 = ₹ 405 at 10% loss ⇒ CP = 405 / 0.90 = ₹ 450
• New SP_2 = ₹ 465

Concept / Approach: Profit% (or loss%) is always measured on CP: (SP − CP)/CP * 100.

Step-by-Step Solution:

Verification / Alternative check: At SP_1 = 405, loss% = (450 − 405)/450 * 100 = 10% (consistent). At SP_2 = 465, result is a small profit ≈ 3.33%.

Why Other Options Are Wrong: 10% profit, 6% loss, and no profit no loss contradict the computed margin; 3.33% loss has the wrong sign.

Common Pitfalls: Using SP as the base instead of CP; profit and loss percentages are always on CP unless explicitly stated otherwise.

Final Answer: profit of 3.33%