In triangle pqr, c is the centroid.

a. if cy = 10, find pc and py
b. if qc = 10, find zc and zq
c. if px = 20, find pq

Because point C is the centroid of the triangle, therefore:

Segments PZ = ZR;  RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:     

PC = 20     

PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:     

ZC = 5       

ZQ = 15

C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
     

PQ = 40

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the answer is 489

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