Three successive discounts of 30% on the marked piece of an item are together equivalent to a single discount of.

The correct option is 65.7%.

To find the single equivalent discount of three successive discounts of 30%, let us assume the initial marked price of the item is 100.

After the first discount of 30%, the price becomes:
$$100-(30\%\text{ of }100)=100-30=70$$

After the second discount of 30%, the price becomes:
$$70-(30\%\text{ of }70)=70-21=49$$

After the third discount of 30%, the final price becomes:

The total discount amount on the original price of 100 is:
$$100-34.3=65.7$$

Since the initial marked price was 100, a total discount of 65.7 is equivalent to a single discount of 65.7%.