If he gains Rs. 75 on an item, what is the cost price of the item?
Calculate Trader's Cost Price with Markup and Discount
This solution details how to determine the original cost price of goods based on markup, discount, and profit information.
Key Concepts Defined
- Cost Price (CP): The initial price paid for the item.
- Marked Price (MP): The price set by the trader, calculated as CP plus a percentage markup.
- Selling Price (SP): The final price after applying a discount to the MP.
- Profit: The gain realized, calculated as SP - CP.
Solving for Cost Price (CP)
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Determine the Marked Price (MP): The trader marks the price 40% above the CP.
MP = CP + (40% of CP) = CP \times (1 + 0.40) = 1.40 \times \text{CP}
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Calculate the Selling Price (SP): A 25% discount is applied to the MP.
SP = MP - (25% of MP) = MP \times (1 - 0.25) = 0.75 \times \text{MP}
Substitute the expression for MP from Step 1:
SP = 0.75 \times (1.40 \times \text{CP}) = 1.05 \times \text{CP}
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Calculate the Profit Percentage relative to CP:
Profit = SP - CP = (1.05 \times \text{CP}) - \text{CP} = 0.05 \times \text{CP}
This means the profit is 5% of the Cost Price.
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Find the Cost Price (CP): Given that the profit is Rs. 75.
We have the equation: 0.05 \times \text{CP} = 75
Solve for CP:
\text{CP} = \frac{75}{0.05} = \frac{75}{5/100} = 75 \times \frac{100}{5} = 75 \times 20
\text{CP} = 1500
Therefore, the cost price of the item is Rs. 1500.
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