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