Loss Calculation:
Let's assume the cost price of 12 marbles is x rupees.
According to the given information, the shopkeeper sells 12 marbles for 1 rupee, which means the selling price of 12 marbles is 1 rupee.
We know that Selling Price (SP) = Cost Price (CP) - Loss (L)
So, 1 = x - L

Loss Percentage Calculation:
The loss percentage is given as 20%. We can calculate the loss using the formula:
Loss Percentage (L%) = (Loss/CP) × 100
Substituting the given values, we get:
20 = (L/x) × 100
Simplifying this equation, we have:
L = 20x/100
L = x/5

Equating Loss and Loss Percentage:
We can equate the two equations we obtained for loss:
x - L = x/5
Multiplying both sides by 5 to eliminate the denominator, we get:
5x - 5L = x
4x = 5L
x = (5/4)L

Calculating the Selling Price to Gain 20%:
To gain 20% in the transaction, the shopkeeper needs to sell the marbles at a price that gives him a profit of 20%. Let's assume the selling price required is y rupees.
Profit Percentage (P%) = (Profit/CP) × 100
Given that the profit percentage is 20%, we can write:
20 = (Profit/x) × 100
Simplifying this equation, we have:
Profit = 20x/100
Profit = x/5

Equating Profit and Profit Percentage:
We can equate the profit obtained with the profit percentage equation:
y - x = x/5
Multiplying both sides by 5, we get:
5y - 5x = x
4x = 5y
x = (5/4)y

Since the selling price required to gain 20% is y rupees, we can write:
x = (5/4)y = (5/4) × 1 = 5/4

Calculating the Marbles for 1 Rupee:
We know that the selling price of 12 marbles is 1 rupee.
If the selling price of x marbles is 5/4 rupees, then we can calculate the number of marbles for 1 rupee as follows:
12/x = 1/(5/4)
12/x = 4/5
Cross-multiplying, we get:
12 * 5 = 4 * x
60 = 4x
x = 15

Therefore, the shopkeeper should sell the marbles at the rate of 15 marbles for 1 rupee to gain a profit of 20%. However, none of the given options match this answer. Hence, the correct answer should be none of these.