Amanda is making pastry dough. She mixes 1/3 of a cup of flour and 1/5 of a cup of sugar. If she wants to mix flour and sugar in the same ratio to make 16 cups of pastry dough, how many cups of flour and sugar will she need?

To find the amount of flour and sugar needed to make 16 cups of pastry dough in the same ratio as Amanda's original mixture, we first need to determine the ratio of flour to sugar in the original mixture.

The original amounts are:
- Flour: \( \frac{1}{3} \) cup
- Sugar: \( \frac{1}{5} \) cup

To find the ratio of flour to sugar, we can express it as:
\[
\text{Ratio of flour to sugar} = \frac{\frac{1}{3}}{\frac{1}{5}} = \frac{1}{3} \times \frac{5}{1} = \frac{5}{3}
\]
This means for every 5 parts of flour, there are 3 parts of sugar.

Next, we can find the total parts in the ratio:
\[
5 + 3 = 8 \text{ parts}
\]

We want to make a total of 16 cups of dough. We can find out how much each part is worth:
\[
\text{Value of each part} = \frac{16 \text{ cups}}{8 \text{ parts}} = 2 \text{ cups per part}
\]

Now, we can calculate the amounts of flour and sugar needed:
- For flour (5 parts):
\[
5 \text{ parts} \times 2 \text{ cups/part} = 10 \text{ cups of flour}
\]
- For sugar (3 parts):
\[
3 \text{ parts} \times 2 \text{ cups/part} = 6 \text{ cups of sugar}
\]

Thus, to maintain the same ratio while making 16 cups of pastry dough, Amanda will need:
- 10 cups of flour
- 6 cups of sugar

Therefore, the answer is:
**B. 10 cups of flour and 6 cups of sugar**.