Question

If a : b = 3 : 1 and b : c = 5 : 1 then find the value of

(i) ${\left(\frac{a^3}{15b^{2}c}\right)}^3$ (ii) $\frac{a^2}{7bc}$

Answer 1

a : b = 3 : 1

$\therefore \frac{a}{b}=\frac{3}{1}\Rightarrow a=3b$ .....(1)

b : c = 5 : 1

$\therefore \frac{b}{c}=\frac{5}{1}\Rightarrow b=5c$ .....(2)

From (1) and (2), we have

a = 3 × 5c = 15c

(i)
$$\begin{gathered} {\left(\frac{a^3}{15b^{2}c}\right)}^3 \\ ={\left[\frac{{\left(15c\right)}^3}{15\times {\left(5c\right)}^2\times c}\right]}^3 \\ ={\left(\frac{15\times 15\times 15c^3}{15\times 25c^2\times c}\right)}^3 \\ ={\left(9\right)}^3 \\ =729 \end{gathered}$$
(ii)
$$\begin{gathered} \frac{a^2}{7bc} \\ =\frac{{\left(15c\right)}^2}{7\times 5c\times c} \\ =\frac{225}{35} \\ =\frac{45}{7} \end{gathered}$$