If the selling price of 11 pencils is equal to the cost price of 15 pencils, find the approximate profit or loss percent.

Options

A. 48.4 % profit
B. 36.8 % loss
C. 40.8 % loss
D. 36.4 % profit

Answer

To find the approximate profit or loss percent based on the given information, we can follow these steps:

### Step 1: Define Variables
Let the cost price (CP) of one pencil be \( x \).

### Step 2: Calculate Total Cost Price
The cost price of 15 pencils is:
\[ \text{Total CP of 15 pencils} = 15x \]

### Step 3: Calculate Selling Price
According to the problem, the selling price (SP) of 11 pencils is equal to the cost price of 15 pencils. Therefore:
\[ \text{Total SP of 11 pencils} = 15x \]

### Step 4: Calculate Selling Price of One Pencil
To find the selling price of one pencil, we divide the total selling price of 11 pencils by 11:
\[ \text{SP of one pencil} = \frac{15x}{11} \]

### Step 5: Calculate Profit or Loss
Now, we can find the profit or loss by comparing the selling price and cost price of one pencil:
\[ \text{Profit or Loss} = \text{SP} - \text{CP} = \frac{15x}{11} - x \]
To simplify this, we can express \( x \) in terms of a common denominator:
\[ \text{Profit or Loss} = \frac{15x}{11} - \frac{11x}{11} = \frac{15x - 11x}{11} = \frac{4x}{11} \]

### Step 6: Calculate Profit or Loss Percentage
To find the profit or loss percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{\frac{4x}{11}}{x} \right) \times 100 = \left( \frac{4}{11} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \frac{400}{11} \approx 36.36\% \]

### Conclusion
Thus, the approximate profit percentage is **36.36%**.

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