The price of a product after a 20% discount is Rs 3024, and this amount already includes 5% tax on the selling price. What was the original marked price of the product in rupees before discount and tax?

Introduction / Context:
This problem combines the ideas of discount and tax on the same product. Many entrance and competitive exams test whether a student can correctly unwind both effects to recover the original marked price before any discount or tax is applied.

Given Data / Assumptions:

• Marked price of the product = unknown (let it be M).
• Discount on marked price = 20 percent.
• Tax on selling price after discount = 5 percent.
• Final price paid by the customer after discount and tax = Rs 3024.
• Tax is calculated on the reduced price after discount, not on the original marked price.

Concept / Approach:
When a discount and then a tax are applied, the final price can be written as: Final price = Marked price * (1 - discount percent) * (1 + tax percent) We are given the final price and both percentages, so we can treat this as an equation in one variable, solve for the marked price M, and then compare with the options.

Step-by-Step Solution:
Step 1: Let the marked price be M. Step 2: After a 20 percent discount, selling price before tax = M * (1 - 20/100) = M * 0.80. Step 3: On this selling price, a 5 percent tax is added, so final price = M * 0.80 * (1 + 5/100) = M * 0.80 * 1.05. Step 4: Multiply the factors: 0.80 * 1.05 = 0.84. Step 5: Therefore, final price = M * 0.84. Step 6: Given final price = Rs 3024, so M * 0.84 = 3024. Step 7: Solve for M: M = 3024 / 0.84. Step 8: Divide to get M = Rs 3600.

Verification / Alternative check:
Take the marked price as Rs 3600 and reapply the operations to confirm. After 20 percent discount: 3600 * 0.80 = Rs 2880. Tax at 5 percent on 2880 is 2880 * 0.05 = Rs 144. Final price = 2880 + 144 = Rs 3024, which matches the given amount. So the marked price of Rs 3600 is correct.

Why Other Options Are Wrong:
2742: This value is too low and would not reach 3024 after discount and tax. 2880: This is actually the price after discount but before tax, not the marked price. 3780: This is higher than required and would result in a final price greater than Rs 3024. 3200: This does not satisfy the relation 3024 = 0.84 * M when checked directly.

Common Pitfalls:
A typical mistake is to subtract or add percentages directly without using multiplication factors. Another error is to treat tax as being applied on the original marked price instead of on the discounted selling price. Students may also forget that a discount reduces the price, while tax increases the price, so both operations must be applied in the correct order using multiplication factors like 0.80 and 1.05.

Final Answer:
The original marked price of the product is Rs 3600.