Rotomac produces very fine quality of writing pens. Company, knows that on an average `10%` of the produced opens are always defective, so are rejected before packing. Company promises to deliver 7200 pens to its wholesaler at ₹ 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. ₹ 6
B. ₹ 7.2
C. ₹ 5.6
D. ₹ 8

Answer

To find the manufacturing cost of each pen produced by Rotomac, we can follow these steps:

### Step 1: Determine the total number of pens produced
Given that 10% of the pens are defective, this means that 90% of the pens are non-defective. If the company promises to deliver 7200 pens, we can set up the following equation:

Let \( x \) be the total number of pens produced.

\[ 0.9x = 7200 \]

### Step 2: Solve for \( x \)
To find \( x \), we can rearrange the equation:

\[ x = \frac{7200}{0.9} = 8000 \]

### Step 3: Calculate the total selling price
The selling price per pen is ₹10. Therefore, the total selling price for 7200 pens is:

\[ \text{Total Selling Price} = 7200 \times 10 = ₹72000 \]

### Step 4: Determine the overall profit
The company estimates an overall profit of 25%. This means that the selling price is 125% of the cost price. Let \( C \) be the total cost price for all pens produced.

We can express this as:

\[ \text{Total Selling Price} = \text{Cost Price} + \text{Profit} \]

Since profit is 25% of the cost price, we can write:

\[ 72000 = C + 0.25C \]

This simplifies to:

\[ 72000 = 1.25C \]

### Step 5: Solve for \( C \)
Now, we can solve for \( C \):

\[ C = \frac{72000}{1.25} = ₹57600 \]

### Step 6: Calculate the manufacturing cost of each pen
To find the manufacturing cost of each pen, we divide the total cost price by the total number of pens produced:

\[ \text{Cost Price per pen} = \frac{C}{x} = \frac{57600}{8000} = ₹7.20 \]

### Final Answer
The manufacturing cost of each pen is **₹7.20**.

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