A man bought 20 pens for Rs.x and the man sold each pen at the cost price of two pens.
If he sold the pen at a loss of 20%, then he would have sold each pen for Rs.36 less.
Find the total selling price of all pens, if he had sold each pen at a profit of 30%.

Let's break down the problem step by step.

### Step 1: Define Variables
- Let the cost price (CP) of each pen be \( y \) Rs.
- Therefore, the total cost price for 20 pens is \( 20y = x \) Rs.

### Step 2: Understand Selling Price at a Loss
- He sold each pen at the cost price of two pens, so the selling price (SP) of each pen is \( 2y \) Rs.
- The loss is 20%, so the loss per pen is \( 0.20 \times y \) Rs.
- Hence, the selling price with a 20% loss would be \( y - 0.20y = 0.80y \) Rs.
- According to the problem, this selling price is Rs.36 less than \( 2y \).

### Step 3: Formulate the Equation
- The equation based on the above information is:
\[
0.80y = 2y - 36
\]
- Solving for \( y \):
\[
0.80y = 2y - 36
\]
\[
2y - 0.80y = 36
\]
\[
1.20y = 36
\]
\[
y = \frac{36}{1.20} = 30 \text{ Rs.}
\]

### Step 4: Find the Total Selling Price at 30% Profit
- Now, if he sold each pen at a 30% profit, the selling price of each pen would be:
\[
\text{SP per pen} = y + 0

Learn how to calculate the total selling price of 20 pens based on cost price, selling price, profit, and loss in this math problem solution. Explore step-by-step calculations for determining selling prices under different scenarios. Suitable for high school students and math enthusiasts.

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