What is the effective single discount equivalent to two successive discounts of 20% and 25% on an article?

Introduction / Context:
Here we are dealing with two successive discounts and asked to find a single discount that produces the same final selling price. Many people initially think that discounts simply add, but that is incorrect because each discount is applied to a reduced base. Understanding effective discount is important in retail mathematics and competitive exam questions dealing with price reductions.

Given Data / Assumptions:
First discount = 20 percent.
Second discount = 25 percent, applied after the first discount.
We need the equivalent single discount on the original marked price.
We can assume a convenient marked price, for example 100 units, because results are based on percentages.

Concept / Approach:
After a 20 percent discount, 80 percent of the original price remains, which is a factor of 0.80. After a further 25 percent discount, the customer pays 75 percent of the already reduced price, a factor of 0.75. The overall remaining fraction is the product 0.80 * 0.75. The effective discount D_eq is found by comparing this final fraction with the original whole, using the relation final fraction = 1 - D_eq / 100. Solving for D_eq gives the effective discount percentage.

Step-by-Step Solution:
Assume marked price = 100 units. After a 20 percent discount, remaining price = 100 * (1 - 0.20) = 100 * 0.80 = 80 units. After an additional 25 percent discount, remaining price = 80 * (1 - 0.25) = 80 * 0.75 = 60 units. So final price after both discounts is 60 units out of the original 100 units. Thus the total reduction = 100 - 60 = 40 units. Effective discount percentage = (40 / 100) * 100 = 40 percent.

Verification / Alternative check:
Using the remaining fraction method, we can confirm the same result. Remaining fraction after both discounts = 0.80 * 0.75 = 0.60. Then 1 - D_eq / 100 = 0.60, implying D_eq / 100 = 0.40, so D_eq = 40 percent. This method shows that the effective discount is independent of the initial assumed marked price and is purely a result of the given percentage reductions.

Why Other Options Are Wrong:
An effective discount of 45 percent would imply a final price of 55 units, but our calculation shows that the final price is 60 units. A 50 percent effective discount would reduce the price to 50 units, which is too low. A 60 percent discount would leave only 40 units to be paid, which is much smaller than 60. Only 40 percent agrees with the computed overall effect of both discounts.

Common Pitfalls:
The main mistake is to simply add the two discounts and state that the effective discount is 45 percent (20 percent + 25 percent). This overlooks the fact that the second discount is applied to an already reduced price, not to the original marked price. Another error is mixing up remaining fractions with discount fractions. To avoid these, always multiply the remaining fractions, find the final fraction of the original price, and compute the single discount as one minus this fraction expressed as a percentage.

Final Answer:
The effective single discount equivalent to successive discounts of 20 percent and 25 percent is 40%.