An article is sold after two successive discounts of 20% and 35% on its marked price.\nIf the final selling price is Rs. 50,700, what is the marked price (in rupees) of the article?

Introduction / Context:
This question involves successive discounts, a standard topic in percentage based word problems. When more than one discount is applied in sequence, you cannot simply add the percentages; instead, you must apply each discount multiplicatively to the current price. Here, you know the final selling price after two discounts and must work backwards to find the original marked price.

Given Data / Assumptions:

• Let the marked price (MP) be M.
• First discount = 20% on M.
• Second discount = 35% on the reduced price after the first discount.
• Final selling price after both discounts = Rs. 50,700.
• We must compute M, the original marked price.

Concept / Approach:
A 20% discount means the buyer pays 80% of the marked price, or 0.80M. Then a 35% discount applied to this reduced price means the buyer pays 65% of that value, or 0.65 * (0.80M). The combined effect is therefore 0.80 * 0.65 = 0.52 of the original marked price. Hence, selling price = 0.52M. We set 0.52M equal to 50,700 and solve for M by simple division.

Step-by-Step Solution:
Step 1: After the first discount of 20%, the price becomes 80% of M = 0.80M. Step 2: After the second discount of 35%, the price becomes 65% of the reduced price = 0.65 * 0.80M. Step 3: Compute the combined factor: 0.65 * 0.80 = 0.52. Step 4: Therefore, final selling price SP = 0.52M. Step 5: Given that SP = Rs. 50,700, we have 0.52M = 50,700. Step 6: Solve for M: M = 50,700 / 0.52. Step 7: Convert to fraction: 0.52 = 52 / 100, so M = 50,700 * 100 / 52. Step 8: Simplify 50,700 / 52 = 975, so M = 975 * 100 = 97,500. Step 9: Thus, the marked price is Rs. 97,500.

Verification / Alternative check:
Check by applying both discounts to Rs. 97,500. First discount 20%: discount amount = 0.20 * 97,500 = 19,500. New price after first discount = 97,500 − 19,500 = 78,000. Second discount 35%: discount amount = 0.35 * 78,000 = 27,300. Final selling price = 78,000 − 27,300 = 50,700, which matches the given value. This confirms that the marked price is correctly found.

Why Other Options Are Wrong:
92,500; 98,500; 94,000; 90,000: Applying successive discounts of 20% and 35% to any of these values does not result in exactly Rs. 50,700. They correspond to different final prices and therefore do not satisfy the equation 0.52M = 50,700.

Common Pitfalls:
A common mistake is to add the two discounts directly, claiming that a 20% and 35% discount together make a 55% discount, and then using 45% as the multiplicative factor. This is wrong because the second discount is applied to a reduced price, not the original. Another error is to miscalculate the product of 0.80 and 0.65. Always convert each discount to its remaining fraction (like 0.80 and 0.65) and then multiply them to get the combined factor.

Final Answer:
The marked price of the article is Rs. 97,500.