A person bought a pens at 25 for a rupee and sold at 15 for a rupee . What is his profit per cent ?

Options

A. `16(2)/(3)%`
B. `33(1)/(3)%`
C. `66(2)/(3)%`
D. `40%`

Answer

To find the profit percentage, we need to determine the cost price (CP) and selling price (SP) of the pens.

### Step 1: Calculate the Cost Price (CP)
The person bought 25 pens for 1 rupee. Therefore, the cost price for one pen is:
\[ \text{CP} = \frac{1 \text{ rupee}}{25 \text{ pens}} = \frac{1}{25} \text{ rupees per pen} \]

### Step 2: Calculate the Selling Price (SP)
The person sold 15 pens for 1 rupee. Therefore, the selling price for one pen is:
\[ \text{SP} = \frac{1 \text{ rupee}}{15 \text{ pens}} = \frac{1}{15} \text{ rupees per pen} \]

### Step 3: Calculate Profit
Profit is calculated as:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values we found:
\[ \text{Profit} = \frac{1}{15} - \frac{1}{25} \]
To subtract these fractions, we need a common denominator. The least common multiple of 15 and 25 is 75. Therefore:
\[ \text{Profit} = \left(\frac{5}{75} - \frac{3}{75}\right) = \frac{2}{75} \text{ rupees per pen} \]

### Step 4: Calculate Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{\frac{2}{75}}{\frac{1}{25}}\right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = \left(\frac{2}{75} \times \frac{25}{1}\right) \times 100 = \left(\frac{50}{75}\right) \times 100 = \frac{2000}{75} \approx 26.67\% \]

### Final Answer
The profit percentage is approximately **26.67%**.