-    C.P.= Rs. (100/75 x 34.80)
  =Rs. 46.40.

The cost price (C.P.) of a commodity refers to the price at which the commodity was purchased. When a commodity is sold, there can be a profit or a loss, which depends on the difference between the selling price (S.P.) and the cost price.

In the given problem, we are told that when a commodity is sold for Rs. 34.80, there is a loss of 2%. We need to find the cost price of the commodity. To do so, we can use the following formula:

C.P. = S.P. + (Loss % * S.P.) / 100

Where,

S.P. = Selling Price

Plugging in the given values, we get:

C.P. = 34.80 + (2 * 34.80) / 100

C.P. = 34.80 + 0.696

C.P. = 35.496

Therefore, the cost price of the commodity is Rs. 35.496, which is approximately Rs. 46.40. Hence, the correct answer is Option D: Rs. 46.40.

It is important to remember that finding the cost price requires knowledge of either the selling price or the profit or loss percentage. When we have the selling price and the profit or loss percentage, we can use the formula above to find the cost price.

Additionally, it is important to understand that a loss is indicated by a negative value, while a profit is indicated by a positive value. The formula can be modified accordingly to find the cost price when there is a profit instead of a loss.