Question

Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt if its marked price is 850?

• A. 650
• B. 720
• C. 700
• D. 680

Hint:

The direct formula \( \text{CP} = \text{MP} \times \frac{100 - \text{Discount \%}}{100 + \text{Profit \%}} \) is very efficient for problems relating Cost Price, Marked Price, Discount, and Profit. Ensure to correctly substitute percentages.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem asks to find the cost price (CP) of a shirt, given its marked price (MP), the discount percentage allowed, and the profit percentage earned.

Step 2: Key Formula or Approach:
1. Calculate the Selling Price (SP) after the discount on the Marked Price (MP).
\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount \%}}{100}\right) \]
2. Use the Selling Price (SP) and Profit Percentage to find the Cost Price (CP).
\[ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit \%}}{100}} \]
Alternatively, a direct relation between CP, MP, Discount%, and Profit% is:
\[ \text{CP} = \text{MP} \times \frac{100 - \text{Discount \%}}{100 + \text{Profit \%}} \]

Step 3: Detailed Explanation:
Given:
- Marked Price (MP) = Rs. 850.
- Discount Percentage = 4%.
- Profit Percentage = 20%.
Method 1: Step-by-step calculation
1. Calculate the Selling Price (SP):
\[ \text{SP} = 850 \times \left(1 - \frac{4}{100}\right) \]
\[ \text{SP} = 850 \times (1 - 0.04) \]
\[ \text{SP} = 850 \times 0.96 \]
\[ \text{SP} = \text{Rs. } 816 \]
2. Calculate the Cost Price (CP):
\[ \text{CP} = \frac{\text{SP}}{1 + \frac{20}{100}} \]
\[ \text{CP} = \frac{816}{1 + 0.20} \]
\[ \text{CP} = \frac{816}{1.20} \]
\[ \text{CP} = \text{Rs. } 680 \]
Method 2: Using the direct formula
\[ \text{CP} = \text{MP} \times \frac{100 - \text{Discount \%}}{100 + \text{Profit \%}} \]
\[ \text{CP} = 850 \times \frac{100 - 4}{100 + 20} \]
\[ \text{CP} = 850 \times \frac{96}{120} \]
\[ \text{CP} = 850 \times \frac{4}{5} \]
\[ \text{CP} = 170 \times 4 \]
\[ \text{CP} = \text{Rs. } 680 \]

Step 4: Final Answer:
The cost price of the shirt is Rs. 680.

Answer 2

Another way to solve this is to test each candidate cost price directly: apply a 20% profit to it and see which one lands on the actual discounted selling price of the shirt.

1. 650: Adding a 20% profit gives a selling price of \( 650 \times 1.20 = 780 \). The actual selling price after the 4% discount on the marked price of 850 is \( 850 \times 0.96 = 816 \), and 780 does not equal 816, so this cost price is incorrect.
2. 720: With a 20% profit, the selling price would be \( 720 \times 1.20 = 864 \), which is higher than the required 816, so this is also not correct.
3. 700: With a 20% profit, the selling price would be \( 700 \times 1.20 = 840 \), still not equal to 816.
4. 680: With a 20% profit, the selling price would be \( 680 \times 1.20 = 816 \), which exactly matches the discounted marked price. This is the correct cost price.

Testing the options against the required selling price of Rs. 816 shows that only a cost price of Rs. 680 gives exactly a 20% profit at that price.

Therefore, the correct answer is 680.