40 A series of three discount rates are provided by a manufacturer to a distributor. The first two of these discount rates are $30 \%$ and $20 \%$. The single discount rate equivalent to all three of the rates is $66.4 \%$. What is the third discount rate? Answer $=\square \%$ (as a percentage rounded to two decimal places)

Step 1 ：Let's denote the initial price as \(P = 1\).

Step 2 ：After the first discount of \(30\% \), the price becomes \(P1 = P \times 0.7 = 0.7\).

Step 3 ：After the second discount of \(20\% \), the price becomes \(P2 = P1 \times 0.8 = 0.56\).

Step 4 ：The price after all three discounts, which is equivalent to a single discount of \(66.4\% \), is \(P3 = P \times (1 - 0.664) = 0.336\).

Step 5 ：We can find the third discount by calculating the difference between the price after the first two discounts and the final price. This gives us \(discount3 = 1 - (P3 / P2) = 0.4\).

Step 6 ：Converting this to a percentage and rounding to two decimal places, we get the third discount rate as \(discount3\_percent = round(discount3 \times 100, 2) = 40.00\% \).

Step 7 ：Final Answer: The third discount rate is \(\boxed{40.00 \%}\).