A TV was sold at a profit of 5%. If it had been sold at a profit of 10%, the profit would have been ₹1,000 more. Find the cost price (CP) of the TV in ₹ by using the difference in profit percentages.

Introduction / Context:
This profit and loss question tests understanding of profit percentage on cost price. The key idea is that the difference between two profit scenarios (10% profit versus 5% profit) is simply the difference in profit percentages applied to the same cost price. Because the cost price does not change, the extra profit amount directly corresponds to an extra 5% of the cost price. Once you set up that relationship, the cost price can be found in one clean division. These problems are common in aptitude because they reward seeing the shortcut rather than calculating two separate selling prices first.

Given Data / Assumptions:

• Profit at first sale = 5% of CP • Profit at second (hypothetical) sale = 10% of CP • Difference in profit amounts = ₹1,000 • Required: cost price (CP)

Concept / Approach:
Profit difference percentage = 10% - 5% = 5%. So the extra ₹1,000 profit equals 5% of CP. Write: 5% of CP = 1000. Convert 5% to fraction: 5% = 5/100 = 1/20. So (1/20)*CP = 1000, hence CP = 1000 * 20 = 20000.

Step-by-Step Solution:
1) Compute the difference in profit percentages: 10% - 5% = 5% 2) This difference corresponds to the extra profit amount: 5% of CP = ₹1,000 3) Convert 5% to a fraction: 5% = 5/100 = 1/20 4) Form the equation: (1/20) * CP = 1000 5) Multiply both sides by 20: CP = 1000 * 20 = 20000 6) Therefore the cost price is ₹20,000.

Verification / Alternative check:
If CP = 20,000: 5% profit = 0.05 * 20,000 = 1,000. 10% profit = 0.10 * 20,000 = 2,000. Difference = 2,000 - 1,000 = 1,000, which matches the condition. So CP = 20,000 is correct.

Why Other Options Are Wrong:
• ₹5,000: 5% of 5,000 is only 250, not 1,000. • ₹10,000: 5% is 500, not 1,000. • ₹15,000: 5% is 750, not 1,000. • ₹25,000: 5% is 1,250, which would make the difference ₹1,250, not ₹1,000.

Common Pitfalls:
• Applying profit percent on selling price instead of cost price. • Calculating selling prices unnecessarily instead of using the percentage difference shortcut. • Treating the ₹1,000 as 5% of selling price rather than 5% of CP.

Final Answer:
₹20,000