Answer :
Sure, let's solve the problem step-by-step:
### Step 1: Calculate the Total Initial Cost
First, we need to calculate the initial cost of all the gel pens that the stationer bought.
The stationer bought 80 gel pens at Rs 30 each:
[tex]\[ \text{Initial Cost} = 80 \times 30 = Rs\ 2400 \][/tex]
### Step 2: Calculate the Number of Pens Left after Theft
Next, we need to determine how many pens are left after 20 pens were stolen:
[tex]\[ \text{Pens Left} = 80 - 20 = 60 \][/tex]
### Step 3: Calculate the Cost of the Remaining Pens
Now we'll calculate the total cost of the 60 pens that are left:
[tex]\[ \text{Cost of Remaining Pens} = 60 \times 30 = Rs\ 1800 \][/tex]
### Step 4: Calculate the Total Selling Price after 5% Loss
The stationer sold the remaining 60 pens at a 5% loss. To find the selling price after the loss, we'll first determine what 5% of the cost of the remaining pens is:
[tex]\[ \text{Loss} = 0.05 \times 1800 = Rs\ 90 \][/tex]
Now, we subtract the loss from the cost of the remaining pens to get the total selling price:
[tex]\[ \text{Total Selling Price} = 1800 - 90 = Rs\ 1710 \][/tex]
### Step 5: Calculate the Selling Price per Pen
Finally, to find the selling price of each remaining pen, we'll divide the total selling price by the number of pens left:
[tex]\[ \text{Selling Price per Pen} = \frac{1710}{60} = Rs\ 28.50 \][/tex]
### Summary
- Initial cost: Rs 2400
- Pens left after theft: 60
- Cost of the remaining pens: Rs 1800
- Total selling price after 5% loss: Rs 1710
- Selling price per pen: Rs 28.50
So, the selling price of each gel pen is Rs 28.50.
### Step 1: Calculate the Total Initial Cost
First, we need to calculate the initial cost of all the gel pens that the stationer bought.
The stationer bought 80 gel pens at Rs 30 each:
[tex]\[ \text{Initial Cost} = 80 \times 30 = Rs\ 2400 \][/tex]
### Step 2: Calculate the Number of Pens Left after Theft
Next, we need to determine how many pens are left after 20 pens were stolen:
[tex]\[ \text{Pens Left} = 80 - 20 = 60 \][/tex]
### Step 3: Calculate the Cost of the Remaining Pens
Now we'll calculate the total cost of the 60 pens that are left:
[tex]\[ \text{Cost of Remaining Pens} = 60 \times 30 = Rs\ 1800 \][/tex]
### Step 4: Calculate the Total Selling Price after 5% Loss
The stationer sold the remaining 60 pens at a 5% loss. To find the selling price after the loss, we'll first determine what 5% of the cost of the remaining pens is:
[tex]\[ \text{Loss} = 0.05 \times 1800 = Rs\ 90 \][/tex]
Now, we subtract the loss from the cost of the remaining pens to get the total selling price:
[tex]\[ \text{Total Selling Price} = 1800 - 90 = Rs\ 1710 \][/tex]
### Step 5: Calculate the Selling Price per Pen
Finally, to find the selling price of each remaining pen, we'll divide the total selling price by the number of pens left:
[tex]\[ \text{Selling Price per Pen} = \frac{1710}{60} = Rs\ 28.50 \][/tex]
### Summary
- Initial cost: Rs 2400
- Pens left after theft: 60
- Cost of the remaining pens: Rs 1800
- Total selling price after 5% loss: Rs 1710
- Selling price per pen: Rs 28.50
So, the selling price of each gel pen is Rs 28.50.
