Two successive discounts of 25% each are given on the marked price of an article. A single discount equivalent to these two successive discounts must be equal to what percentage?

Introduction / Context:
This problem is about converting two successive percentage discounts into one equivalent single discount. It tests the understanding that successive percentage changes are multiplicative in effect and cannot be combined by simple addition. Such questions appear frequently in competitive exams within the percentage and discount chapter.

Given Data / Assumptions:

• There are two discounts applied successively, each of 25%.
• We want to find a single discount rate that gives the same final price.
• No information about the actual marked price is needed because the result is percentage based.

Concept / Approach:
If a discount of d% is given, the price becomes (1 - d/100) times the original. For successive discounts d1% and d2%, the combined reduction factor is (1 - d1/100) * (1 - d2/100). To find the equivalent single discount D%, we set (1 - D/100) equal to that product and solve for D. In this question both discounts are 25%, so the calculation simplifies nicely.

Step-by-Step Solution:
Step 1: First discount of 25% leaves 75% of the price, so factor = 0.75. Step 2: Second discount of 25% again leaves 75% of the current price, so second factor = 0.75. Step 3: Combined factor after two discounts = 0.75 * 0.75 = 0.5625. Step 4: This means the customer finally pays 56.25% of the original price. Step 5: Therefore, the total effective discount = 100% - 56.25% = 43.75%. Step 6: So the single equivalent discount is 43.75%.

Verification / Alternative check:
Take a convenient marked price, say Rs 100. After the first 25% discount, price becomes 100 - 25 = 75. After the second 25% discount, price becomes 75 - 18.75 = 56.25. So the loss in price is 100 - 56.25 = 43.75. This confirms the computed single discount of 43.75%.

Why Other Options Are Wrong:

• 56.25: This is the final percentage of price paid, not the percentage discount.
• 50: Adding 25% and 25% directly would give 50%, but that ignores the multiplicative nature of successive discounts.
• 45: This is an approximation, not the exact value.
• 40: This is lower than the correct discount and does not match the actual effect.

Common Pitfalls:
The most common mistake is to simply add the percentages and claim that two 25% discounts equal a 50% discount, which is incorrect. Another error is to take the average of percentages. The correct technique is always to convert percentages to decimal factors, multiply them, and then convert back. Using a trial marked price of 100 is a very helpful method to visualise and verify results quickly.

Final Answer:
Two successive discounts of 25% each are equivalent to a single discount of 43.75% on the original price.