Recovering cost price from selling price and profit percent A radio is sold for Rs 1980 at a gain of 10%. What was its cost price?

Introduction / Context:
Given SP and profit %, cost price is found by dividing by (1 + profit%). This is a standard reverse-percentage operation in profit and loss.

Given Data / Assumptions:

• SP = Rs 1980.
• Profit % = 10% = 0.10.

Concept / Approach:
SP = CP × (1 + profit%). Therefore, CP = SP / 1.10.

Step-by-Step Solution:
CP = 1980 / 1.10 = 1800.

Verification / Alternative check:
10% of 1800 = 180; SP = 1800 + 180 = 1980 (confirms).

Why Other Options Are Wrong:
1782 is 10% off 1980 (wrong base); 2178 is higher than SP; 1650 and 1880 fail the 10% forward check.

Common Pitfalls:
Taking 10% of SP rather than CP when reversing, or dividing by 0.10 instead of 1.10.

Final Answer:
Rs 1800