Profit and Loss – Two selling prices with a stated difference in gain rates: By selling a radio for Rs 475 instead of Rs 451, the percentage gain increases by 6%. What is the cost price of the radio?

Introduction / Context:
When a fixed rupee increase in selling price causes a fixed percentage-point increase in gain, the difference between the two gains can be written in terms of cost price. This leads to a simple linear equation in CP.

Given Data / Assumptions:

• Selling price 1 = Rs 451
• Selling price 2 = Rs 475
• Gain2% − Gain1% = 6 percentage points

Concept / Approach:
Gain% = (SP − CP) / CP * 100. The difference between gain percentages equals (SP2 − SP1) / CP * 100. Use the given 6% and solve for CP.

Step-by-Step Solution:
(475 − 451) / CP * 100 = 624 / CP = 0.06CP = 24 / 0.06 = 400

Verification / Alternative check:
At CP = 400: Gain1% = (451 − 400)/400 * 100 = 12.75%; Gain2% = (475 − 400)/400 * 100 = 18.75%; difference is 6%.

Why Other Options Are Wrong:
434 and 440.50 do not give exactly a 6% difference. 420 is close but incorrect. “None” is false.

Common Pitfalls:
Confusing 6% of selling price with 6 percentage points of gain.

Final Answer:
Rs 400