A wholesaler sells toys at a profit of `20%` to a retailer and retailer sells these toys to its customer at a profit of `25%`. What is the profit percentage of the retailer at orignal cp?

Options

A. `5%`
B. `80%`
C. `20 %`
D. `25%`

Answer

To find the profit percentage of the retailer based on the original cost price, we can break down the problem step by step.

### Step 1: Understand the Wholesaler's Selling Price
The wholesaler sells toys at a profit of 20%. This means if the cost price (CP) of the toys for the wholesaler is \( CP_w \), the selling price (SP) for the wholesaler is calculated as follows:

\[ SP_w = CP_w + (20\% \text{ of } CP_w) = CP_w + 0.2 \times CP_w = 1.2 \times CP_w \]

### Step 2: Determine the Retailer's Selling Price
The retailer buys the toys from the wholesaler at the selling price \( SP_w \) and sells them at a profit of 25%. Therefore, if the cost price for the retailer is \( CP_r = SP_w \), the selling price for the retailer is:

\[ SP_r = CP_r + (25\% \text{ of } CP_r) = CP_r + 0.25 \times CP_r = 1.25 \times CP_r \]

### Step 3: Substitute the Wholesaler's Selling Price
Now, substituting \( CP_r \) with \( SP_w \):

\[ SP_r = 1.25 \times SP_w = 1.25 \times (1.2 \times CP_w) = 1.25 \times 1.2 \times CP_w \]

### Step 4: Calculate the Selling Price of the Retailer
Calculating the multiplication:

\[ SP_r = 1.5 \times CP_w \]

### Step 5: Calculate the Profit of the Retailer
The profit made by the retailer is given by:

\[ \text{Profit} = SP_r - CP_r = SP_r - SP_w \]

Substituting the values we have:

\[ \text{Profit} = (1.5 \times CP_w) - (1.2 \times CP_w) = (1.5 - 1.2) \times CP_w = 0.3 \times CP_w \]

### Step 6: Calculate the Profit Percentage
The profit percentage is calculated as:

\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP_r} \right) \times 100 = \left( \frac{0.3 \times CP_w}{1.2 \times CP_w} \right) \times 100 \]

Simplifying this gives:

\[ \text{Profit Percentage} = \left( \frac{0.3}{1.2} \right) \times 100 = 25\% \]

### Final Answer
The profit percentage of the retailer based on the original cost price is **25%**.

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