A bought an article, paying 5% less than the original price. A sold it with 20% profit on the price he had paid. What percent of profit did A earn on the origi nal price?

Options

A. (A) 0.1
B. (B) 0.13
C. (C) 0.14
D. `(D) 17/2` %

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Original Price
Let the original price of the article be denoted as \( P \).

### Step 2: Calculate the Price A Paid
A bought the article at 5% less than the original price. Therefore, the price A paid can be calculated as:
\[ \text{Price paid by A} = P - 0.05P = 0.95P \]

### Step 3: Calculate the Selling Price
A sold the article at a 20% profit on the price he paid. The selling price can be calculated as:
\[ \text{Selling Price} = \text{Price paid by A} + 20\% \text{ of Price paid by A} \]
\[ \text{Selling Price} = 0.95P + 0.20 \times 0.95P = 0.95P + 0.19P = 1.14P \]

### Step 4: Calculate the Profit Earned
The profit earned by A can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Price paid by A} = 1.14P - 0.95P = 0.19P \]

### Step 5: Calculate the Profit Percentage on the Original Price
To find the profit percentage based on the original price, we can use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Original Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{0.19P}{P} \right) \times 100 = 19\% \]

### Final Answer
A earned a profit of **19%** on the original price.

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