Rajeshwar bought 16 dozen ball point pens and sold them by and by. Due to a calculation mistake in fixing selling price, he lost an amount equal to S.P. of 4 dozen pens. Find the loss per cent. Find the S.P. of one dozen pens, if he purchased these 16 dozen pens for 240.

Options

A. 18
B. 10
C. 12
D. 14

Answer

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

### Step 1: Calculate the Cost Price (C.P.) of 1 dozen pens.
Rajeshwar bought 16 dozen pens for 240 rupees.

\[ \text{C.P. of 1 dozen pens} = \frac{\text{Total C.P.}}{\text{Number of dozens}} = \frac{240}{16} = 15 \text{ rupees} \]

### Step 2: Determine the Selling Price (S.P.) of 16 dozen pens.
Let the selling price of 1 dozen pens be \( x \) rupees. Therefore, the selling price of 16 dozen pens will be:

\[ \text{S.P. of 16 dozen pens} = 16x \text{ rupees} \]

### Step 3: Calculate the loss incurred.
According to the problem, Rajeshwar lost an amount equal to the selling price of 4 dozen pens.

\[ \text{Loss} = \text{S.P. of 4 dozen pens} = 4x \text{ rupees} \]

### Step 4: Set up the equation for loss.
The loss can also be calculated as:

\[ \text{Loss} = \text{C.P.} - \text{S.P.} = 240 - 16x \]

Setting the two expressions for loss equal to each other:

\[ 240 - 16x = 4x \]

### Step 5: Solve for \( x \).
Rearranging the equation gives:

\[ 240 = 16x + 4x \]
\[ 240 = 20x \]
\[ x = \frac{240}{20} = 12 \text{ rupees} \]

### Step 6: Calculate the loss.
Now we can find the total loss:

\[ \text{Loss} = 4x = 4 \times 12 = 48 \text{ rupees} \]

### Step 7: Calculate the loss percentage.
The loss percentage can be calculated using the formula:

\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{C.P.}} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{48}{240} \right) \times 100 = 20\% \]

### Final Results:
- Selling Price of 1 dozen pens: 12 rupees
- Loss Percentage: 20%

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