A shop offers two successive discounts of 40% on the marked price of an article.\nThese two consecutive discounts together are equivalent to a single discount of what percentage on the original marked price?

Introduction / Context:
This question focuses on the concept of successive discounts, which are very common in shopping and sales scenarios. When two discounts are applied one after another, the net discount is not simply the sum of the two percentages. Instead, each discount applies to the price resulting from the previous discount. Understanding how to compute the combined effect is essential in profit and loss, commercial maths, and real life decision making about offers and sales.

Given Data / Assumptions:

• The shop offers a first discount of 40% on the marked price.
• Then a second discount of 40% is applied on the already reduced price.
• We want to find the single equivalent discount percentage that would produce the same final price when applied directly to the original marked price.
• Marked price is assumed to be some positive value, which we can denote by M.

Concept / Approach:
Successive discounts are represented with multiplicative factors. A discount of 40% leaves 60% of the price, which corresponds to multiplying the price by 0.60. Two such discounts in a row multiply to 0.60 * 0.60. The result is a combined multiplier that tells us what fraction of the marked price the customer ultimately pays. The equivalent single discount is then 100% minus this final percentage paid. This method is systematic and avoids errors that occur when percentages are simply added.

Step-by-Step Solution:
Step 1: Let the marked price be M. Step 2: After the first discount of 40%, the customer pays 60% of M, which is 0.60 * M. Step 3: After the second discount of 40% on the reduced price, the customer pays 60% of the new price. Step 4: Therefore final price = 0.60 * (0.60 * M) = 0.60 * 0.60 * M. Step 5: Multiply 0.60 by 0.60 to get 0.36. Step 6: So the final price is 0.36 * M, which means the customer pays 36% of the marked price. Step 7: The equivalent single discount is 100% minus 36% = 64%. Step 8: Hence two successive discounts of 40% are equal to one discount of 64%.

Verification / Alternative check:
Choose a convenient marked price, for example M = Rs 100. First discount of 40% reduces the price to 60, since 40% of 100 is 40 and 100 minus 40 is 60. A second discount of 40% on 60 reduces it by 24 to 36. So the final price after two discounts is Rs 36. If a single discount were applied to 100 to produce the same final price, that discount would be 100 - 36 = 64. This confirms the algebraic result and shows that the combined discount rate is indeed 64%.

Why Other Options Are Wrong:
Option a, 80%, comes from the incorrect idea of simply adding 40% and 40%, which does not account for the reduced base after the first discount. Option b, 96%, would correspond to paying only 4% of the price, which is far lower than the actual 36%. Option d, 72%, suggests paying 28% of the price, which is also inconsistent with the computed final price of 36%. Only 64% accurately reflects the combined effect of two successive 40% discounts.

Common Pitfalls:
The most common error is to assume that two discounts of x% each add up to a total discount of 2x%. This ignores that the second discount is applied to a lower price. Another mistake is failing to convert percentages to decimal multipliers before multiplying. Always remember that with successive percentage changes you work with factors of the form (1 minus discount rate) repeatedly, and then convert the final factor back into an equivalent percentage.

Final Answer:
Two successive discounts of 40% are equivalent to a single discount of 64% on the marked price.