Step 1: Recall the two price indices.
Both Laspeyres and Paasche compare today's prices with a base year, but they differ in the weights they use.
Step 2: Pin down Laspeyres.
The Laspeyres index fixes the basket at base year quantities,
\[ P_L=\frac{\sum p_1 q_0}{\sum p_0 q_0}\times100 \]
So it uses base year quantities as weights. That matches option C.
Step 3: Pin down Paasche.
The Paasche index uses current year quantities,
\[ P_P=\frac{\sum p_1 q_1}{\sum p_0 q_1}\times100 \]
So tying base year weights to Paasche, as option D does, is wrong.
Step 4: Drop the CPI and PPI mix ups.
CPI tracks consumer goods, not raw materials, and PPI tracks producer goods, not consumer goods. So options A and B swap the names and are wrong.
\[ \boxed{\text{Laspeyres uses base year quantities as weights}} \]