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 $\frac{abc}{def}$ ?

• A. $\frac{3}{8}$
• B. $\frac{27}{8}$
• C. $\frac{3}{4}$
• D. $\frac{27}{4}$

Answer 1

Answer: (A)

$\frac{3}{8}$

Given
$\frac{a}{b}=\frac{1}{3}\Rightarrow a=\frac{b}{3}$

$\frac{b}{c}=2\Rightarrow c=\frac{b}{2}$

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

$\frac{d}{e}=3\Rightarrow e=\frac{d}{3}\Rightarrow e=\frac{b}{3}$

$\frac{e}{f}=\frac{1}{4}\Rightarrow f=4e\Rightarrow f=\frac{4b}{3}$

$\therefore \frac{abc}{def}=\frac{\frac{b}{3}\times b\times \frac{b}{2}}{b\times \frac{b}{3}\times \frac{4b}{3}}=\frac{3}{8}$