Given information:
- The shopkeeper sold a certain amount of pens at a 20% profit.
- The shopkeeper sold a certain amount of pencils at a 5% loss.
- Overall, the shopkeeper made a profit of 360 rupees.

Objective:
Determine the number of pens the shopkeeper sold.

Assumptions:
- The cost price of each pen and pencil is the same.
- The cost price is denoted as "x" rupees.

Step 1: Calculate the profit from selling pens
- Let's assume the shopkeeper sold "y" pens.
- Profit from selling each pen = 20% of the cost price = (20/100) * x = 0.2x
- Total profit from selling pens = 0.2x * y

Step 2: Calculate the loss from selling pencils
- Let's assume the shopkeeper sold "z" pencils.
- Loss from selling each pencil = 5% of the cost price = (5/100) * x = 0.05x
- Total loss from selling pencils = 0.05x * z

Step 3: Calculate the overall profit
- Overall profit = Total profit from selling pens - Total loss from selling pencils = 0.2x * y - 0.05x * z
- Given, the overall profit is 360 rupees.
- Therefore, 0.2x * y - 0.05x * z = 360

Step 4: Solve the equation
- We need to find the value of "y" (number of pens sold).
- We have one equation with two variables (y and z).
- To solve this, we need another equation.
- Let's assume the number of pencils sold is "p".
- Therefore, y + p = total number of items sold (unknown).

Step 5: Substitute the value of p
- We know that the total number of items sold = y + p = y + z (since we assumed p = z)
- Substitute this value in the equation derived in Step 3:
- 0.2x * y - 0.05x * (y + z) = 360
- Simplify the equation:
- 0.2x * y - 0.05x * y - 0.05x * z = 360
- 0.15x * y - 0.05x * z = 360

Step 6: Substitute values and solve the equation
- We need the value of "x" to solve the equation.
- Unfortunately, we do not have enough information to find the value of "x".
- Therefore, without the value of "x", we cannot find the exact number of pens sold (y).

Conclusion:
- Without the value of "x", we cannot determine the exact number of pens sold (y).