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A businessman allows a discount of 10% on the marked price. What percent above the cost price must he mark his goods to make a profit of 17 percent?
एक व्यापारी अंकित मूल्य पर 10% की छूट देता है। उसे 17% का लाभ कमाने के लिए अपने सामान के लागत मूल्य से कितने प्रतिशत अधिक मल्य अंकित करना होगा?

A

`20%`

B

`27%`

C

`18%`

D

`30%`

Text Solution

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The correct Answer is:
To solve the problem, we need to determine how much above the cost price the businessman must mark his goods in order to achieve a profit of 17% after giving a discount of 10% on the marked price. ### Step-by-Step Solution: 1. **Define the Cost Price (CP)**: Let the cost price (CP) of the goods be represented as \( CP = 100 \) (for simplicity). 2. **Calculate the Selling Price (SP) for a 17% Profit**: To find the selling price (SP) that gives a profit of 17%, we use the formula: \[ SP = CP + (Profit \% \times CP) \] Substituting the values: \[ SP = 100 + (17\% \times 100) = 100 + 17 = 117 \] 3. **Determine the Marked Price (MP)**: The businessman allows a discount of 10% on the marked price (MP). The selling price is related to the marked price by the formula: \[ SP = MP - (Discount \% \times MP) \] Since the discount is 10%, we can express this as: \[ SP = MP - (10\% \times MP) = MP \times (1 - 0.10) = MP \times 0.90 \] Therefore, we can rearrange this to find the marked price: \[ MP = \frac{SP}{0.90} \] Substituting the selling price we found earlier: \[ MP = \frac{117}{0.90} = 130 \] 4. **Calculate the Percentage Above the Cost Price**: Now, we need to find out how much the marked price is above the cost price in percentage terms. The formula for percentage increase is: \[ \text{Percentage Increase} = \left(\frac{MP - CP}{CP}\right) \times 100 \] Substituting the values we have: \[ \text{Percentage Increase} = \left(\frac{130 - 100}{100}\right) \times 100 = \left(\frac{30}{100}\right) \times 100 = 30\% \] ### Final Answer: The businessman must mark his goods **30% above the cost price** to achieve a profit of 17% after allowing a 10% discount on the marked price. ---
To solve the problem, we need to determine how much above the cost price the businessman must mark his goods in order to achieve a profit of 17% after giving a discount of 10% on the marked price. ### Step-by-Step Solution: 1. **Define the Cost Price (CP)**: Let the cost price (CP) of the goods be represented as \( CP = 100 \) (for simplicity). 2. **Calculate the Selling Price (SP) for a 17% Profit**: ...
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