On its anniversary, a showroom offers an 18% discount on the marked price of bikes. Raghuram buys a bike for Rs. 54,540 after discount. What is the marked price of the bike?

Introduction / Context:
This is a typical discount and marked price problem from the topic of percentage and profit and loss. The showroom gives a fixed discount rate on the marked price, and the buyer pays the discounted price. We are given the final price paid and the discount percentage, and we must work backwards to find the original marked price. Such questions are very common in retail and commerce related aptitude tests.

Given Data / Assumptions:

Let the marked price of the bike be M rupees.

A discount of 18% is offered on this marked price.

So, the selling price after discount is 82% of M, since 100% - 18% = 82%.

Raghuram pays Rs. 54,540 for the bike.

Therefore, 82% of M equals 54,540.

Concept / Approach:
We express the discounted price as a percentage of the marked price. If a discount of d% is given, the buyer pays (100 - d)% of the marked price. In this case, the buyer pays 82% of M. Thus we set up the equation (82 / 100) * M = 54,540 and solve for M by dividing 54,540 by 0.82. This is a simple reverse percentage calculation.

Step-by-Step Solution:
Let the marked price be M.Discount = 18% of M.Selling price after discount = M - 0.18M = 0.82M.We are given that the selling price is Rs. 54,540.So, 0.82M = 54,540.Therefore, M = 54,540 / 0.82.Compute: 54,540 / 0.82 ≈ 66,512.20.Rounded to the nearest rupee, M ≈ Rs. 66,512.

Verification / Alternative check:
Verify using the option Rs. 66,512 as the marked price. Discount at 18% of 66,512 is 0.18 * 66,512 ≈ 11,972.16. Subtracting this from the marked price gives 66,512 - 11,972.16 ≈ 54,539.84, which rounds to 54,540. This matches the given selling price. The slight difference is due to rounding to the nearest rupee, and the option Rs. 66,512 is therefore the correct marked price.

Why Other Options Are Wrong:

Rs. 63,548, Rs. 65,000, Rs. 67,857 and Rs. 70,500, when reduced by 18%, do not give a selling price of approximately Rs. 54,540.

Only Rs. 66,512, when reduced by 18%, yields a discounted price that matches the amount paid by Raghuram.

Common Pitfalls:
Some students mistakenly add 18% to the selling price instead of reversing from the marked price. Others compute 18% of 54,540 instead of 18% of the unknown marked price. Another common mistake is to divide 54,540 by 18 or by 0.18 directly, which does not correspond to the relationship between discount and selling price. Always remember that selling price = (100 - discount percentage) percent of marked price and set up the equation accordingly.

Final Answer:
The marked price of the bike before the 18% discount was approximately Rs. 66512.