Two successive discounts of 15 percent and 35 percent are given on the same marked price of an article. What is the single equivalent net discount percentage that would give the same final price?

Introduction / Context:
This problem deals with successive discounts, which do not simply add up. When two discounts are applied one after another, the net effect is less than the sum of the individual discounts. The question asks for the single equivalent discount that produces the same final price as the two given discounts applied successively.

Given Data / Assumptions:

• First discount = 15 percent.
• Second discount = 35 percent.
• Both are applied successively on the same marked price.
• We are required to find one net discount that yields the same final result.

Concept / Approach:
If the marked price is M, after a discount of d1 percent, the price becomes M * (1 − d1 / 100). After a second discount d2 percent on this reduced price, the final price is M * (1 − d1 / 100) * (1 − d2 / 100). The equivalent single discount d satisfies final price = M * (1 − d / 100). We compute the combined factor and then convert it back to a net discount percentage.

Step-by-Step Solution:
Step 1: After 15 percent discount, price factor = 1 − 15 / 100 = 0.85. Step 2: After 35 percent discount on the reduced price, factor = 1 − 35 / 100 = 0.65. Step 3: Final price factor after both discounts = 0.85 * 0.65. Step 4: Compute 0.85 * 0.65 = 0.5525. Step 5: If d is the equivalent discount, then final factor = 1 − d / 100 = 0.5525. Step 6: So d / 100 = 1 − 0.5525 = 0.4475, and d = 44.75 percent.

Verification / Alternative check:
To check, assume a marked price of 100 units. Successive discounts give: first discount leaves 85 units, then second leaves 85 * 0.65 = 55.25 units. This final price equals 55.25 percent of 100, meaning the total discount is 100 − 55.25 = 44.75 percent, matching our calculation.

Why Other Options Are Wrong:

• 51.25, 55.25, and 56.25 all correspond to larger net discounts that would produce a lower final price than the correct combined effect of 15 percent and 35 percent.

Common Pitfalls:
A common mistake is to simply add the two discounts, 15 percent + 35 percent = 50 percent, which is not correct because the second discount is applied to an already reduced price. Always multiply the remaining fractions and then convert back to a single discount to avoid errors.

Final Answer:
The net equivalent discount is 44.75 percent.