📚 Part of: Indian History And Geography Mcqs: Election Dates, Urban Wealth, And Historical Roads

If a person offers two successive discounts of 30% and 40% on an article, then what is the total discount?

Category: Miscellaneous Indian Gk

Correct Answer: D) 58%.

Exam Relevance: CAT, GMAT, GRE, Bank PO, SSC CGL

Difficulty: Moderate

Concept notes:

When two successive discounts are applied to a product, the total discount is not simply the sum of the individual discounts. Instead, the total discount is calculated by applying each discount sequentially to the reduced price. This concept is crucial for understanding how discounts compound and affect the final price.

Common Mistakes:
  • Students often mistakenly add the two discounts together, assuming the total discount is 70% (30% + 40%).
  • Another common mistake is to apply the discounts in reverse order, which can lead to incorrect results.
  • Some students might incorrectly assume that the discounts are applied to the original price sequentially, rather than to the reduced price after the first discount.
Explanation:

To understand the concept of successive discounts, let's consider an example where an article originally costs \( P \) rupees. The first discount is 30%, and the second discount is 40%.

1. **First Discount Calculation:**

- The first discount is 30%, so the price after the first discount is:

\[

P_1 = P - 0.30P = 0.70P

\]

- This means the price is reduced to 70% of the original price.

2. **Second Discount Calculation:**

- The second discount is 40%, but it is applied to the new price \( P_1 \):

\[

P_2 = P_1 - 0.40P_1 = 0.60P_1

\]

- Substituting \( P_1 \) from the first step:

\[

P_2 = 0.60 \times 0.70P = 0.42P

\]

- This means the final price is 42% of the original price.

3. **Total Discount Calculation:**

- The total discount is the difference between the original price and the final price:

\[

\text{Total Discount} = P - P_2 = P - 0.42P = 0.58P

\]

- This means the total discount is 58% of the original price.

Therefore, the total discount when two successive discounts of 30% and 40% are applied is 58%. This is why option D is the correct answer.

It is important to note that the total discount is not simply the sum of the individual discounts (30% + 40% = 70%) because the second discount is applied to the reduced price after the first discount, not the original price. This compounding effect is a key concept in understanding successive discounts.

Option Analysis:
  • Option A: This option is incorrect. The total discount is not simply the sum of the two individual discounts. Adding 30% and 40% would give 70%, but this does not account for the compounding effect of successive discounts. The correct method involves applying each discount sequentially to the reduced price.
  • Option B: This option is incorrect. The total discount is not 70%. This is a common misconception where students add the two discounts together without considering the compounding effect. The correct method involves applying each discount sequentially to the reduced price.
  • Option C: This option is incorrect. The total discount is not 56%. This might be a result of a miscalculation or misunderstanding of how successive discounts work. The correct method involves applying each discount sequentially to the reduced price.
  • Option D: This option is correct. The total discount is 58%. This is calculated by applying the first discount of 30% to the original price, then applying the second discount of 40% to the reduced price after the first discount. This method accounts for the compounding effect of successive discounts.
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