If a/b=1/3, b/c=2, c/d=1/2, d/e=3 and e/f=1/4, then what is the value of a b c/d e f ? · ABC26GN0974

$$\begin{aligned} & \frac{a}{b}=\frac{1}{3} \Rightarrow b=3 a ; \frac{b}{c}=2 \Rightarrow c=\frac{b}{2}=\frac{3 a}{2} ; \\ & \frac{c}{d}=\frac{1}{2} \Rightarrow d=2 c=2\left(\frac{3 a}{2}\right)=3 a ; \\ & \frac{d}{e}=3 \Rightarrow e=\frac{d}{3}=\left(\frac{3 a}{3}\right)=a ; \frac{e}{f}=\frac{1}{4} \Rightarrow f=4 e=4 a . \\ & \therefore \quad \frac{a b c}{d e f}=\frac{(a)(3 a)\left(\frac{3 a}{2}\right)}{(3 a)(a)(4 a)}=\frac{9}{2} a^{3} \times \frac{1}{12 a^{3}}=\frac{3}{8} . \end{aligned}$$