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Question:

If $\frac{a}{b} = \frac{1}{3}$ , $\frac{b}{c} = 2$ , $\frac{c}{d} = \frac{1}{2}$ , $\frac{d}{e} = 3$ and $\frac{e}{f} = \frac{1}{4}$ then what is the value of $\frac{a b c}{d e f}$ ?

Explanation:

$\frac{a}{d}$ = $\frac{a}{b} \times \frac{b}{c} \times \frac{c}{d}$ = $\frac{1}{3} \times 2 \times \frac{1}{2}$ = $\frac{1}{3}$

$\frac{b}{e}$ = $\frac{b}{c} \times \frac{c}{d} \times \frac{d}{e}$ = $2 \times \frac{1}{2} \times 3$ = 3

$\frac{c}{f}$ = $\frac{c}{d} \times \frac{d}{e} \times \frac{e}{f}$ = $\frac{1}{2} \times 3 \times \frac{1}{4}$ = $\frac{3}{8}$

∴ $\frac{a b c}{d e f}$ = $\frac{1}{3} \times 3 \times \frac{3}{8}$ = $\frac{3}{8}$

Hence, option (a).

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