Three successive discounts of 20%, 10% and 30% are allowed on an article. What is the net single discount percentage equivalent to these three discounts?

Introduction / Context:
This question explores the idea of successive discounts and asks for a single equivalent discount that gives the same final price as applying three different discounts one after another. In practical life, retailers sometimes offer multiple discounts, and customers or exam candidates must understand that these discounts do not simply add up. Instead, each discount is applied to the price remaining after the previous discount.

Given Data / Assumptions:
An article is given three successive discounts of 20 percent, 10 percent, and 30 percent.
We are asked to find one equivalent discount that produces the same final price.
No information about the marked price is required because we can assume any convenient initial value, for example 100 units.

Concept / Approach:
If the marked price is M, then after a discount of D percent the price becomes M * (1 - D / 100). For successive discounts, we multiply all the remaining percentage factors. Here, the remaining factors are 80 percent (0.80) after 20 percent, then 90 percent (0.90) after 10 percent, and 70 percent (0.70) after 30 percent. Thus, the final price factor is 0.80 * 0.90 * 0.70. The equivalent single discount D_eq is found from the equation final factor = 1 - D_eq / 100. Solving for D_eq gives the net discount percentage.

Step-by-Step Solution:
Assume marked price = 100 units for simplicity. After first discount of 20 percent, remaining factor = 1 - 0.20 = 0.80. After second discount of 10 percent, new factor = 1 - 0.10 = 0.90. After third discount of 30 percent, new factor = 1 - 0.30 = 0.70. Overall multiplication factor = 0.80 * 0.90 * 0.70. Compute 0.80 * 0.90 = 0.72. Then 0.72 * 0.70 = 0.504. So final price = 100 * 0.504 = 50.4 units. This means the equivalent discount is 100 - 50.4 = 49.6 units on a base of 100 units. Hence net discount percentage = 49.6 percent.

Verification / Alternative check:
We can also express the equivalent discount as D_eq using the formula 1 - D_eq / 100 = product of remaining factors. So 1 - D_eq / 100 = 0.504. Thus D_eq / 100 = 1 - 0.504 = 0.496 and D_eq = 0.496 * 100 = 49.6 percent. This matches the result obtained by applying the assumed marked price of 100 units. Since the calculation uses pure percentages, the result does not depend on the actual marked price.

Why Other Options Are Wrong:
A net discount of 45.2 percent would leave a final factor of 0.548, which is larger than 0.504, so the final price would be higher than it should be. A net discount of 54.6 percent would leave only 45.4 percent of the price, which is too low compared to 50.4 percent. A net discount of 50.4 percent would leave 49.6 percent of the price, which is smaller than the computed 50.4 percent. Only a 49.6 percent discount correctly reflects the combined effect of the three given discounts.

Common Pitfalls:
A very common error is to simply add the three discounts: 20 percent + 10 percent + 30 percent = 60 percent. This ignores the fact that each discount successively reduces the base on which the next discount is calculated. Another trap is rounding intermediate values too aggressively, which can lead to a slightly off final discount. To avoid mistakes, always convert each discount to a remaining factor, multiply these factors, and then convert back to a percentage discount from the original price.

Final Answer:
The net single discount equivalent to the three successive discounts is 49.6 percent.