From loss to gain on the same item: Rajdeep sells a radio for ₹ 768 at a loss of 20%. If he sells (the same model) for ₹ 1,020 instead, what is his profit percentage?

Introduction / Context:Translate a known loss scenario to cost, then evaluate the profit at a different selling price on the same cost base. This is a standard two-step profit–loss conversion.

Given Data / Assumptions:

• SP1 = ₹ 768 at 20% loss ⇒ SP1 = 0.80 * CP.
• Alternative SP2 = ₹ 1,020.

Concept / Approach:CP = SP1 / 0.80. Profit% at SP2 = (SP2 − CP)/CP * 100.

Step-by-Step Solution:CP = 768 / 0.80 = ₹ 960Profit at SP2 = 1,020 − 960 = ₹ 60Profit% = 60 / 960 * 100 = 6.25%

Verification / Alternative check:At SP1, loss = 192 (which is 20% of 960). At SP2, the rupee margin 60 over 960 is exactly 6.25%—consistent.

Why Other Options Are Wrong:

• 5.25% / 7.25% / 8.25%: do not match 60/960 * 100.

Common Pitfalls:

• Mistaking the 20% as a fraction of SP when computing CP; the base is CP.

Final Answer:6.25 %