Two bicycles together cost ₹1,600. If the first is sold at 10% profit and the second at 20% profit, the seller’s revenue is slightly less than if he had interchanged the profit rates (first at 20%, second at 10%) by ₹5. What is the difference between their cost prices?

Introduction / Context:
We compare two selling scenarios with the same pair of bicycles but swapped profit rates. Because total cost is fixed, the only change is how profits are distributed across the two items. The difference between the two total revenues directly reveals the difference in their cost prices.

Given Data / Assumptions:

• Let costs be x and y with x + y = 1,600
• Scenario 1 revenue: 1.10x + 1.20y
• Scenario 2 revenue: 1.20x + 1.10y
• Scenario 2 exceeds Scenario 1 by ₹5

Concept / Approach:
Subtract the two expressions to eliminate common terms: (1.20x + 1.10y) − (1.10x + 1.20y) = 0.10x − 0.10y. Set this equal to ₹5 and solve for (x − y).

Step-by-Step Solution:
0.10(x − y) = 5x − y = 50Therefore, the difference in cost prices is ₹50

Verification / Alternative check:
Let x = 825 and y = 775 (sum 1,600 and difference 50). Scenario 1 SP = 1.10*825 + 1.20*775 = 907.5 + 930 = 1,837.5; Scenario 2 SP = 1.20*825 + 1.10*775 = 990 + 852.5 = 1,842.5; difference = ₹5 — matches.

Why Other Options Are Wrong:
₹25/₹40/₹75 do not satisfy the precise ₹5 revenue difference upon swapping profit rates.

Common Pitfalls:
Attempting to compute individual costs instead of recognizing the neat cancellation; forgetting that only the distribution, not the total cost, changes.

Final Answer:
₹ 50