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 (abc)/(def)?

Question

If \(\frac{a}{b} = \frac13, \frac{b}{c} = 2, \frac{c}{d} = \frac12,\frac{d}{e}=3\)  and \(\frac{e}{f}=\frac14,\) then what is the value of \(\frac{abc}{def}?\)

(a) \(\frac38\) 

(b) \(\frac{27}{8}\)

(c) \(\frac34\)

(d) \(\frac{27}{4}\)

Answer 1

(a) \(\frac38\)

\(\frac{a}{b} = \frac13\) ⇒ a = \(\frac{b}{3}\)

\( \frac{b}{c} = 2\) ⇒ c = \(\frac{b}{2}\)

\( \frac{c}{d} = \frac12\) ⇒ d = 2c ⇒ d = 2 x \(\frac{b}{2}\) = b

\(\frac{d}{e}= 3\) ⇒ e = \(\frac{d}{3}\) ⇒ e = \(\frac{b}{3}\)

\(\frac{e}{f}=\frac14\) ⇒ f  = 4e ⇒ f = \(\frac{4b}{3}\)

∴ \(\frac{abc}{def}\) = \(\frac{\frac{b}{3}\times{b}\times\frac{b}{2}}{b\times\frac{b}{3}\times\frac{4b}{3}}\) = \(\frac38.\)