Calculating Discount Percentage for a Target Gain
To find the required discount percentage, we need to determine the relationship between the cost price (\(CP\)), marked price (\(MP\)), and the selling price (\(SP\)) needed for a specific gain.
Step 1: Assume Cost Price and Calculate Marked Price
Let the Cost Price (\(CP\)) of the item be \(100\).
The shopkeeper fixes the Marked Price (\(MP\)) 20% above the cost price:
\( MP = CP + (20\% \text{ of } CP) \)
\( MP = 100 + (0.20 \times 100) = 100 + 20 = 120 \)
So, the Marked Price is \(120\).
Step 2: Calculate the Selling Price for the Desired Gain
The shopkeeper aims for a gain of 2%.
The required Selling Price (\(SP\)) is calculated on the cost price:
\( SP = CP + (2\% \text{ of } CP) \)
\( SP = 100 + (0.02 \times 100) = 100 + 2 = 102 \)
The target Selling Price is \(102\).
Step 3: Calculate the Discount Amount
The discount is the difference between the Marked Price and the Selling Price.
\( \text{Discount Amount} = MP - SP \)
\( \text{Discount Amount} = 120 - 102 = 18 \)
The discount amount is \(18\).
Step 4: Calculate the Discount Percentage
The Discount Percentage is calculated based on the Marked Price.
\( \text{Discount Percentage} = \left( \frac{\text{Discount Amount}}{MP} \right) \times 100 \% \)
\( \text{Discount Percentage} = \left( \frac{18}{120} \right) \times 100 \% \)
\( \text{Discount Percentage} = \left( \frac{3}{20} \right) \times 100 \% = 15\% \)
Therefore, the shopkeeper should offer a 15% discount.
Similar Questions
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Important Questions from Profit and Loss
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