Question

In a Christmas sale, the prices of Dell Laptops were reduced by 10% for public. However, for Dell employees, the price was further reduced by 5%. If the original price of a laptop was $330 before Christmas sale, approximately how much would it cost in a Christmas sale to a Dell employee?

• A. $271
• B. $277
• C. $282
• D. $287
• E. $295

Hint:

For successive discounts of \(d_1%\) and \(d_2%\), the final price is calculated by applying them one after the other. It is not the same as a single discount of \((d_1 + d_2)%\). A common mistake is to add the percentages (10% + 5% = 15%) and apply a single 15% discount, which would give an incorrect answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem involves successive percentage discounts. A "further" reduction means the second discount is applied to the already discounted price, not the original price.

Step 2: Key Formula or Approach:
To apply a percentage discount, multiply the price by (1 − discount rate).
- Price after 1st discount = Original Price × (1 − 10%)
- Final Price = (Price after 1st discount) × (1 − 5%)

Step 3: Detailed Explanation:
The original price of the laptop is $330.

First Discount (for the public):
The price is reduced by 10%.
Discount amount = 10% of $330 = 0.10 × 330 = $33.
Price after first discount = $330 − $33 = $297.
Alternatively: $330 × (1 − 0.10) = $330 × 0.90 = $297.

Second Discount (for Dell employees):
The price is further reduced by 5%, applied to $297.
Second discount amount = 5% of $297 = 0.05 × 297 = 14.85.
Final price = $297 − $14.85 = $282.15.
Alternatively: $297 × (1 − 0.05) = $297 × 0.95 = $282.15.

Since the question asks for the approximate cost, $282.15 ≈ $282.

Step 4: Final Answer:
The approximate cost for a Dell employee would be $282.