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, you can multiply the price by (1 - discount rate). 
- Price after 1st discount = Original Price \(\times\) (1 - 10%) 
- Final Price = (Price after 1st discount) \(\times\) (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 \(\times\) 330 = \(\$\)33. 
Price after first discount = \(\$\)330 - \(\$\)33 = \(\$\)297. 
Alternatively, Price = \(\$\)330 \(\times\) (1 - 0.10) = \(\$\)330 \(\times\) 0.90 = \(\$\)297. 
Second Discount (for Dell employees): 
The price was further reduced by 5%. This 5% discount is applied to the \(\$\)297 price. 
Second discount amount = 5% of \(\$\)297 = 0.05 \(\times\) 297. 
Calculation: \(0.05 \times 297 = (5/100) \times 297 = 1485/100 = \$14.85\). 
Final price for an employee = \(\$\)297 - \(\$\)14.85 = \(\$\)282.15. 
Alternatively, Final Price = \(\$\)297 \(\times\) (1 - 0.05) = \(\$\)297 \(\times\) 0.95 = \(\$\)282.15. 
The question asks for the approximate cost. \(\$\)282.15 is approximately \(\$\)282. 
 

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