While selling a router, a shopkeeper gives a discount of 15 percent on the marked price. If he instead gives a discount of 20 percent, his profit falls by Rs. 51. What is the original marked price of the router?

Introduction / Context:
This question involves discounts, marked price, and the effect on profit. The shopkeeper changes the discount rate by 5 percentage points, which leads to a fixed change in profit. From the difference in profits we can determine the marked price, since cost price is constant and only the selling price changes.

Given Data / Assumptions:

• Marked price of the router = M (unknown).
• First scenario: discount = 15 percent on M.
• Second scenario: discount = 20 percent on M.
• The difference in profit between the two scenarios = Rs. 51.
• Cost price is constant in both cases.

Concept / Approach:
Profit in each scenario is selling price minus cost price. When the discount on marked price increases from 15 percent to 20 percent, the selling price decreases. The difference in profits between the two scenarios equals the difference between the two selling prices because the cost price does not change. That gives a direct equation linking the marked price and the known profit difference.

Step-by-Step Solution:
Let the marked price be M rupees. Selling price with 15 percent discount: SP1 = M * (1 - 15 / 100) = 0.85 * M. Selling price with 20 percent discount: SP2 = M * (1 - 20 / 100) = 0.80 * M. Difference in selling prices = SP1 - SP2 = 0.85M - 0.80M = 0.05M. Given that this difference in selling prices equals the drop in profit, which is Rs. 51. Therefore 0.05M = 51. M = 51 / 0.05 = 1020 rupees.

Verification / Alternative check:
Marked price M = Rs. 1020. With 15 percent discount: SP1 = 1020 * 0.85 = Rs. 867. With 20 percent discount: SP2 = 1020 * 0.80 = Rs. 816. Difference in selling prices = 867 - 816 = Rs. 51. This matches the given difference in profit, so the marked price is correct.

Why Other Options Are Wrong:
Rs. 1000, Rs. 1040, and Rs. 980: For each of these marked prices, the difference between selling prices with 15 percent and 20 percent discounts would not be exactly Rs. 51. Only Rs. 1020 satisfies the condition that a 5 percentage point change in discount leads to a Rs. 51 change in profit.

Common Pitfalls:
Candidates sometimes incorrectly attempt to include cost price in the equation, even though it cancels out when taking the difference between profits. Another mistake is to treat the 5 percent as 5 rupees instead of 5 percent of the marked price. Always remember that percentage changes must be applied to the relevant base amount, here the marked price.

Final Answer:
The original marked price of the router is Rs. 1020.