Profit Percentage: Cost Price vs. Selling Price

The question asks us to find the profit percentage calculated on the Cost Price (CP) that is equivalent to 20% profit calculated on the Selling Price (SP).

Key Concepts

• Profit ($P$) is the difference between Selling Price ($SP$) and Cost Price ($CP$): $P = SP - CP$.
• Profit Percentage on Cost Price = $\frac{P}{CP} \times 100\%$.
• Profit Percentage on Selling Price = $\frac{P}{SP} \times 100\%$.

Step-by-Step Solution

1. Define Variables and Given Information:

   • Let $CP$ be the Cost Price.
   • Let $SP$ be the Selling Price.
   • Let $P$ be the Profit.
   • We are given that the profit is 20% of the Selling Price: $P = 0.20 \times SP$.

2. Relate Selling Price, Cost Price, and Profit:

   We know the basic relationship: $SP = CP + P$.

   Substitute the given profit expression ($P = 0.20 \times SP$) into this equation:

   $SP = CP + (0.20 \times SP)$

3. Calculate Selling Price in terms of Cost Price:

   Rearrange the equation to find $SP$ in terms of $CP$:

   $SP - 0.20 \times SP = CP$

   $0.80 \times SP = CP$

   $SP = \frac{CP}{0.80}$

   $SP = 1.25 \times CP$

4. Calculate Profit in terms of Cost Price:

   Now substitute the expression for $SP$ back into the profit equation ($P = 0.20 \times SP$):

   $P = 0.20 \times (1.25 \times CP)$

   $P = 0.25 \times CP$

5. Calculate Profit Percentage on Cost Price:

   The profit percentage on the cost price is calculated as:

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

   Substitute the value of $P$ we found:

   Profit % on CP = $\frac{0.25 \times CP}{CP} \times 100\%$

   Profit % on CP = $0.25 \times 100\%$

   Profit % on CP = $25\%$

Therefore, a profit of 20% on the selling price is equivalent to a 25% profit on the cost price.