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?
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?
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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.
Updated On: May 6, 2026
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The Correct Option is D
Solution and Explanation
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.
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.
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