At a discount of 15%, the selling price of a microwave oven is Rs. 34,000.\nWhat would be the selling price of the same microwave oven if the discount is changed to 37.5% on the same marked price?

Introduction / Context:
This question involves working backwards from a discounted selling price to find the marked price, and then applying a different discount to that marked price. It tests your understanding of how discount percentages relate to selling prices, and how to reverse a discount to recover the original marked price. These steps are common in profit and loss and pricing problems.

Given Data / Assumptions:

• At a 15% discount, the selling price (SP1) = Rs. 34,000.
• Let the marked price (MP) be M.
• We know SP1 = M after a 15% reduction, so SP1 = 85% of M.
• We must find the selling price SP2 if the discount is 37.5% on the same marked price M.
• All prices are in rupees and no extra charges or taxes are mentioned.

Concept / Approach:
A discount of 15% means the customer pays 85% of the marked price, that is SP1 = 0.85M. We use the given SP1 to solve for M. Once we have M, we apply 37.5% discount to get the new selling price SP2, which is 62.5% of M (because 100% - 37.5% = 62.5%). So, SP2 = 0.625M. Both steps rely on converting percentage discounts into decimal factors.

Step-by-Step Solution:
Step 1: Represent the first discount: At 15% discount, SP1 = 85% of MP. Step 2: Write the equation: 0.85M = 34,000. Step 3: Solve for M: M = 34,000 / 0.85. Step 4: Compute 34,000 / 0.85 = 40,000. So the marked price M = Rs. 40,000. Step 5: Now consider the new discount: 37.5% discount means the customer pays 62.5% of MP. Step 6: Write SP2 = 62.5% of 40,000 = 0.625 * 40,000. Step 7: Compute 0.625 * 40,000 = 25,000. Step 8: Therefore, at 37.5% discount, the selling price will be Rs. 25,000.

Verification / Alternative check:
We can confirm the marked price by recalculating the original selling price. Marked price M = Rs. 40,000. At 15% discount, discount amount = 0.15 * 40,000 = 6,000, so SP1 = 40,000 - 6,000 = 34,000, matching the problem statement. Then, at 37.5% discount, discount amount = 0.375 * 40,000 = 15,000, giving SP2 = 40,000 - 15,000 = 25,000, which matches our previous calculation exactly.

Why Other Options Are Wrong:
Rs. 15,625: This is far less than the price after a 37.5% discount and would correspond to a much bigger reduction.

Rs. 17,968.75 and Rs. 29,218.75: These numbers do not correspond to a simple percentage such as 37.5% off Rs. 40,000 and likely arise from partial or incorrect factor calculations.

Rs. 30,000: This would correspond to a 25% discount on 40,000, not 37.5%.

Common Pitfalls:
Students sometimes mistakenly subtract 15% and 37.5% directly from the selling price instead of working with the marked price. Another common error is to assume that 34,000 is 15% of the marked price instead of 85%. Always remember that a 15% discount means you pay 85% of the marked price. Converting percentages to factors like 0.85 and 0.625 keeps the reasoning clear.

Final Answer:
If the discount is 37.5%, the selling price of the microwave oven will be Rs. 25,000.