Rotomac produces very fine quality of writing pens. Company knows that on an average 10% of the produced pens are always defective so are rejected before packing. Company promises to deliver 7200 pens to its wholesaler at Rs. 10 each. It estimates the overall profit on all the manufactured pens to be 25%. What is the manufacturing cost of each pen?

Options

A. Rs. 6
B. Rs. 7.2
C. Rs. 5.6
D. Rs. 8

Answer

To find the manufacturing cost of each pen, we will follow these steps:

### Step 1: Determine the total number of pens produced.
Given that 10% of the pens produced are defective, this means that 90% of the pens are good. The company promises to deliver 7200 pens to the wholesaler.

Let the total number of pens produced be \( P \). Since 90% of the produced pens are good, we can express this as:
\[ 0.9P = 7200 \]

### Step 2: Solve for \( P \).
To find \( P \), we rearrange the equation:
\[ P = \frac{7200}{0.9} = 8000 \]
Thus, the total number of pens produced is 8000.

### Step 3: Calculate the selling price (SP).
The selling price per pen is Rs. 10, and the total selling price for 7200 pens is:
\[ SP = 7200 \times 10 = 72000 \]

### Step 4: Determine the profit percentage.
The company estimates an overall profit of 25% on all manufactured pens. The relationship between selling price (SP), cost price (CP), and profit can be expressed as:
\[ SP = CP + \text{Profit} \]
Since the profit is 25% of the cost price, we can express it as:
\[ \text{Profit} = 0.25 \times CP \]
Thus, we can rewrite the equation as:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 5: Set up the equation for cost price.
Substituting the selling price into the equation gives:
\[ 72000 = 1.25 \times CP \]

### Step 6: Solve for \( CP \).
To find the cost price, we rearrange the equation:
\[ CP = \frac{72000}{1.25} = 57600 \]

### Step 7: Calculate the cost price per pen.
Since the total cost price is for 8000 pens, we can find the cost price per pen:
\[ \text{Cost Price per pen} = \frac{57600}{8000} = 7.2 \]

### Final Answer:
The manufacturing cost of each pen is Rs. 7.2.

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