Question Bank › General Aptitude › Simplification › ABC26GN0974ABC26GN0974 · Simplification Subject: General Aptitude · Chapter: Simplification · Exam: 2006 · Marks: · Difficulty:
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 $\frac{a b c}{d e f}$ ?
(a) $\frac{1}{4}$
(b) $\frac{3}{4}$
(c) $\frac{3}{8}$
(d) $\frac{27}{4}$
(e) $\frac{27}{8}$
Answer Explanation $$\begin{aligned} & \frac{a}{b}=\frac{1}{3} \Rightarrow b=3 a ; \frac{b}{c}=2 \Rightarrow c=\frac{b}{2}=\frac{3 a}{2} ; \\ & \frac{c}{d}=\frac{1}{2} \Rightarrow d=2 c=2\left(\frac{3 a}{2}\right)=3 a ; \\ & \frac{d}{e}=3 \Rightarrow e=\frac{d}{3}=\left(\frac{3 a}{3}\right)=a ; \frac{e}{f}=\frac{1}{4} \Rightarrow f=4 e=4 a . \\ & \therefore \quad \frac{a b c}{d e f}=\frac{(a)(3 a)\left(\frac{3 a}{2}\right)}{(3 a)(a)(4 a)}=\frac{9}{2} a^{3} \times \frac{1}{12 a^{3}}=\frac{3}{8} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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