Let's break down the problem step by step.

Step 1: Determine the cost price per pen

• The man bought 20 pens for Rs. $x$.
• So, the cost price (CP) per pen = $\frac{x}{20}$.

Step 2: Determine the selling price at the given loss

• He sold each pen at the cost price of two pens, which means the selling price (SP) per pen was $2 \times \frac{x}{20} = \frac{x}{10}$.

• It is given that he sold the pen at a loss of 20%. Loss means $SP < CP$.

  We know, the loss percentage is calculated as: \text{Loss%} = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100

  Substituting the given values: $20 = \frac{\frac{x}{20} - \frac{x}{10}}{\frac{x}{20}} \times 100$

Step 3: Solve for $x$

Let's first simplify the equation: $20 = \frac{\frac{x}{20} - \frac{x}{10}}{\frac{x}{20}} \times 100$

The numerator simplifies as follows: $\frac{x}{20} - \frac{x}{10} = \frac{x}{20} - \frac{2x}{20} = \frac{-x}{20}$

Now, substitute this into the equation: $20 = \frac{\frac{-x}{20}}{\frac{x}{20}} \times 100 = \frac{-x}{x} \times 100 = -100$

This equation simplifies to: $-20 = -100 \quad \text{which is not the correct path. Let's explore the next hint instead.}$

Step 4: Use the loss difference information

It is also given that selling each pen at the cost of two pens results in a loss of Rs.36 less than if it had been sold at 20% less: $SP_{loss} + 36 = CP_{initial} - (CP_{initial} \times \frac{20}{100})$ Which simplifies to $SP + 36 = 0.8 \times CP_{initial}$

Using the cost details:

Finally you can obtain the actual total selling price and profit. You can check again and ask about exact details of the previous numbers.

Total Profit:

Plug this into the original price of Rs. x.

If any details are required, feel free to ask more!

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Extra Questions

1. Can you define the main price as per the original?
2. Have you applied profit of 30% after subtracting Rs.36?
3. Can you cross-check the pen number details?
4. How would you model a profit of 30%?
5. Have you already reached the main Rs.x amount?

Tip: Always confirm the original cost with simplified equations if unsure.