Find x, when :

(i) 3 : 4 :: 2.4 : x

(ii) 1 : 3 :: x : 7

(iii) x : 1.5 :: 3 : 5

(i) Given,

3 : 4 :: 2.4 : x

Solving for x,

$\Rightarrow \dfrac{3}{4} = \dfrac{2.4}{x} \\[1em] \Rightarrow 3 \times x = 4 \times 2.4 \\[1em] \Rightarrow 3x = 9.6 \\[1em] \Rightarrow x = \dfrac{9.6}{3} \\[1em] \Rightarrow x = 3.2$

Hence, x = 3.2

(ii) Given,

1 : 3 :: x : 7

Solving for x,

$\Rightarrow \dfrac{1}{3} = \dfrac{x}{7} \\[1em] \Rightarrow x = \dfrac{7}{3} = 2\dfrac{1}{3}.$

Hence, x = $2\dfrac{1}{3}$.

(iii) Given,

x : 1.5 :: 3 : 5

Solving for x,

$\Rightarrow \dfrac{x}{1.5} = \dfrac{3}{5} \\[1em] \Rightarrow 5 \times x = 1.5 \times 3 \\[1em] \Rightarrow x = \dfrac{4.5}{5} \\[1em] \Rightarrow x = 0.9$

Hence, x = 0.9