At a 20 percent discount the selling price of an article is 2,400 rupees. What will be the selling price of the same article if the discount is increased to 32.5 percent?

Introduction / Context:
This question combines forward and reverse percentage calculations involving discounts. First, you must recover the marked price from a known selling price at one discount rate, and then use the same marked price to compute a new selling price at a different discount rate. This kind of multi step thinking is very common in profit and loss aptitude questions.

Given Data / Assumptions:
- At 20 percent discount, selling price (SP1) = 2,400 rupees.
- Discount is given on marked price (M).
- We must first find M, then apply a discount of 32.5 percent to find new selling price (SP2).

Concept / Approach:
When a discount of d percent is applied, the customer pays (100 - d) percent of the marked price. So SP1 = (1 - 0.20) * M = 0.80 * M. After finding M from this equation, we apply the second discount of 32.5 percent, so SP2 = (1 - 0.325) * M = 0.675 * M. Working with decimal multipliers makes the steps straightforward.

Step-by-Step Solution:
Step 1: 20 percent discount means the customer pays 80 percent, or 0.80, of the marked price.Step 2: Given SP1 = 2,400 rupees, we have 0.80 * M = 2,400.Step 3: Solve for M: M = 2,400 / 0.80 = 3,000 rupees.Step 4: Now the discount is 32.5 percent, so the customer pays 100 percent - 32.5 percent = 67.5 percent of M.Step 5: In decimal form, 67.5 percent = 0.675.Step 6: New selling price SP2 = 0.675 * 3,000.Step 7: Compute SP2: 0.675 * 3,000 = 2,025 rupees.

Verification / Alternative check:
Check the logic by reversing. If marked price is 3,000 rupees, then at 20 percent discount, the price is 0.80 * 3,000 = 2,400, which matches the given condition. At 32.5 percent discount, the amount of discount is 0.325 * 3,000 = 975 rupees. Subtracting this from 3,000 gives 3,000 - 975 = 2,025 rupees, agreeing with the earlier calculation.

Why Other Options Are Wrong:
- 2,125 and 2,225 rupees correspond to smaller discounts than 32.5 percent on a 3,000 rupee article.
- 2,325 rupees is closer to the original selling price at 20 percent discount and does not reflect the larger discount of 32.5 percent.

Common Pitfalls:
One frequent mistake is to apply the new discount directly on the old selling price of 2,400 rupees instead of on the marked price. Discounts always apply to the marked price, not to the previous selling price. Another error is to add or subtract percentages directly without converting them into multiplicative factors on the marked price.

Final Answer:
The new selling price at a 32.5 percent discount is 2,025 rupees.