If two times A is equal to three times of B and also equal to four times of C, then A : B : C is

$$\eqalign{ & 2A = 3B \cr & Or,\,B = \left( {\frac{2}{3}} \right)A;\,{\text{and}} \cr & 2A = 4C \cr & Or,\,C = \left( {\frac{1}{2}} \right)A; \cr & {\text{Hence}}, \cr & A:B:C = A:\frac{{2A}}{3}:\frac{A}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1:\frac{2}{3}:\frac{1}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6:4:3 \cr} $$