Let G1,G2,G3 be the centroids of the triangular faces OBC,OCA,OAB of a tetrahedron OABC . If V1 denote the volume of the tetrahedron OABC and V2 that of  the parallelopiped with OG1,OG2,OG3 as three  concurrent edges, then :

Taking O as the origin,let the position vectors of A,B and C be a→,b→ and c→ respectively. Then the position vectors ofG1,G2 and G3 are b→+c→3,c→+a→3 and a→+b→3  respectively. ∴                      V1  =  16 a→ b→ c→ and  V2=OG1→OG2→OG3→ Now,  V2=OG1→OG2→OG3→⇒                    V2  = b→ +c→3 c→ +a→ 3 a→ +b→3⇒                 V2  =127 b→ +c→  c→ + a→ a→ +b→⇒                 V2  =227  a→ b→ c→⇒                 V2  =227 × 6V1   ⇒  9 V2 = 4V1 Hence,   (a) is the correct answer.