An article is sold for Rs 16896 after two successive discounts of 20% and 12% are applied on its marked price. What is the marked price of the article in rupees?

Introduction / Context:

This question extends the idea of successive discounts. Instead of asking for the net discount, it gives the final selling price after discounts and asks you to recover the marked price. These reverse percentage problems are common in competitive exams and require careful handling of discount factors.

Given Data / Assumptions:

• First discount = 20% on the marked price.
• Second discount = 12% on the already reduced price.
• Final selling price after both discounts = Rs 16896.
• We need to find the original marked price M.

Concept / Approach:

Each discount reduces the price by a certain factor. A 20% discount leaves 80% of the price, which is a factor 0.80. A 12% discount leaves 88% of the price, which is a factor 0.88. Multiplying these factors gives the fraction of the marked price that the customer actually pays. Then we set this fraction of M equal to the final selling price and solve for M.

Step-by-Step Solution:

Verification / Alternative check:

Check using the found marked price. If M = Rs 24000, then after a 20% discount the price is 80% of 24000, which is Rs 19200. After a further 12% discount, the price becomes 88% of 19200, that is 0.88 * 19200 = Rs 16896. This matches the given selling price exactly, so the marked price is confirmed.

Why Other Options Are Wrong:

• 22000 and 21500: When you apply 20% and 12% discounts on these values, the final price is lower than 16896.
• 23800: The final price after both discounts will be slightly below the required 16896.
• 20000: After successive discounts, this would give a final price much lower than 16896.

Common Pitfalls:

The most frequent mistake is to subtract 20% and 12% directly from the marked price or to treat the total discount as 32%. Another error is to divide the selling price by incorrect factors, such as 0.68 or 0.80 alone. Always remember that successive discounts multiply as factors, and reverse problems require you to divide by the combined factor to get back to the original price.

Final Answer:

The marked price of the article is Rs 24000.