Which is better: a single discount of 70%, or two successive discounts of 40% and 30% on the marked price?

Introduction / Context:
This discount problem compares a single large discount with two smaller successive discounts. Many customers and even shopkeepers sometimes get confused about whether two successive discounts are equivalent to a simple sum of the percentages, and whether they match a single large discount. This question helps clarify how successive discounts work and which option gives a lower final price.

Given Data / Assumptions:

• Option 1: A single discount of 70% on the marked price.
• Option 2: Two successive discounts of 40% and 30% on the same marked price.
• We assume the same marked price P for fair comparison.
• We need to determine which option yields a larger discount (that is, lower final price).

Concept / Approach:
Discounts are applied multiplicatively, not additively. A single discount of 70% means the customer pays 30% of the marked price. Two successive discounts mean we first reduce the price by 40%, then reduce the remaining amount by 30%. To compare, we express the final price as a fraction or percentage of the original marked price P in both cases. The option with the smaller final price is the better discount from the customer perspective.

Step-by-Step Solution:
Step 1: Let the marked price be P. Step 2: Under a single 70% discount, customer pays 30% of P. Step 3: Final price with 70% discount = 30% of P = 0.30 * P. Step 4: Under successive discounts, first discount is 40%, so new price = 60% of P = 0.60 * P. Step 5: Second discount is 30% on the reduced price, so final price = 70% of 0.60 * P. Step 6: Final price under successive discounts = 0.70 * 0.60 * P = 0.42 * P. Step 7: Compare the final prices: 0.30 * P versus 0.42 * P. Step 8: Clearly, 0.30 * P is less than 0.42 * P, so the single 70% discount gives a lower price. Step 9: Therefore, the 70% discount is better for the buyer.

Verification / Alternative check:
We can choose a convenient numerical marked price, for example P = 100. For the 70% discount, the customer pays 30% of 100 = 30. For the successive discounts, after 40% discount, price is 60, and then after 30% discount on 60, the customer pays 70% of 60 = 42. Since 30 is less than 42, paying 30 is better from the customer perspective. This simple example confirms that a single 70% discount is more beneficial than successive 40% and 30% discounts.

Why Other Options Are Wrong:
Saying 40% is better or that both are the same ignores the multiplicative nature of successive discounts. Two discounts of 40% and 30% do not add to 70%; they result in an effective discount of 1 - 0.42 = 58%. Therefore their combined effect is smaller than a single 70% discount. The option "None" and "Depends on the marked price" are incorrect because the comparison holds for any positive marked price, not just specific values.

Common Pitfalls:
A frequent mistake is to simply add the successive discounts, claiming that 40% + 30% equals 70% and thinking they are equivalent to a single 70% discount. This is incorrect because the second discount is applied to the already reduced price, not the original. Another pitfall is to compare only the discount percentages and not the final paid amounts. Always compute final prices as a fraction of the marked price to make accurate comparisons.

Final Answer:
A single discount of 70% is better than successive discounts of 40% and 30% on the same marked price.