Understanding Profit Calculation: CP vs SP

This question asks us to determine the profit percentage calculated on the cost price (CP) when we know the profit percentage is based on the selling price (SP). It's a common scenario in business math where profit margins might be discussed differently.

Key Terms Explained

• Cost Price (CP): The initial amount paid to acquire an item.
• Selling Price (SP): The price at which the item is sold to a customer.
• Profit: The financial gain, calculated as SP minus CP (assuming SP > CP).
• Profit % on SP: Profit calculated as a percentage of the Selling Price. The formula is $\frac{\text{Profit}}{\text{SP}} \times 100$.
• Profit % on CP: Profit calculated as a percentage of the Cost Price. The formula is $\frac{\text{Profit}}{\text{CP}} \times 100$.

Step-by-Step Calculation

To find the profit percentage on the cost price, we can follow these steps:

1. Assume a Selling Price (SP):

   Let's assume the Selling Price (SP) is $100$. This makes percentage calculations straightforward.

2. Calculate Profit using the given SP Profit %:

   The question states the profit is $20\%$ on the selling price.

   Profit = $20\%$ of SP

   Profit = $\frac{20}{100} \times 100 = 20$

3. Determine the Cost Price (CP):

   We know the relationship: SP = CP + Profit.

   Therefore, we can find the CP: CP = SP - Profit.

   CP = $100 - 20 = 80$

4. Calculate Profit % on Cost Price (CP):

   Now, we calculate the profit percentage based on the Cost Price.

   Profit % on CP = $\frac{\text{Profit}}{\text{CP}} \times 100$

   Using the values we found:

   Profit % on CP = $\frac{20}{80} \times 100$

5. Simplify the Result:

   First, simplify the fraction $\frac{20}{80}$ which equals $\frac{1}{4}$.

   Profit % on CP = $\frac{1}{4} \times 100 = 25\%$

Final Answer Derivation

The calculation shows that if the profit is $20\%$ on the selling price, the profit is $25\%$ on the cost price. This aligns with the first option provided.