Profit and Loss – From a small loss to a gain with a fixed price jump: A radio is sold at a loss of 2.5%. Had it been sold for Rs 100 more, there would have been a 7.5% gain. For a 12.5% gain, at what price should it be sold?

Introduction / Context:
We are given two conditions that tie selling prices to percentages of cost. These allow the cost price to be found first, and then a target selling price for a desired profit percentage can be computed.

Given Data / Assumptions:

• At first sale: SP1 = 97.5% of CP = 0.975 * CP
• If SP increases by Rs 100: SP2 = SP1 + 100 = 1.075 * CP
• Target: SP for 12.5% gain = 1.125 * CP

Concept / Approach:
From SP1 + 100 = 1.075 * CP and SP1 = 0.975 * CP, subtract to obtain 100 = 0.10 * CP. Then compute CP and plug into 1.125 * CP.

Step-by-Step Solution:
100 = (1.075 − 0.975) * CP = 0.10 * CPCP = 100 / 0.10 = 1000SP for 12.5% gain = 1.125 * 1000 = Rs 1125

Verification / Alternative check:
At CP 1000, a Rs 100 increase from 0.975 * 1000 = 975 to 1075 indeed represents a change from 2.5% loss to 7.5% gain.

Why Other Options Are Wrong:
850 and 925 are below the loss or moderate gain scenarios; 1080 is not equal to 12.5% above 1000; 1000 is CP, not a 12.5% gain.

Common Pitfalls:
Adding or subtracting percentages directly, rather than converting to multiplicative relations around CP.

Final Answer:
Rs 1125