Find the value of x in the following proportions :

(i) 10 : 35 = x : 42

(ii) 3 : x = 24 : 2

(iii) 2.5 : 1.5 = x : 3

(iv) x : 50 :: 3 : 2.

(i) Given, 10 : 35 = x : 42

$\Rightarrow \dfrac{10}{35} = \dfrac{x}{42} \\[0.5em] \Rightarrow x = \dfrac{10}{35} \times 42 \\[0.5em] \Rightarrow x = \dfrac{420}{35} \\[0.5em] \Rightarrow x = 12.$

Hence, the value of x = 12.

(ii) Given, 3 : x = 24 : 2

$\Rightarrow \dfrac{3}{x} = \dfrac{24}{2} \\[0.5em] \Rightarrow x = \dfrac{3}{24} \times 2 \\[0.5em] \Rightarrow x = \dfrac{6}{24} \\[0.5em] \Rightarrow x = \dfrac{1}{4}.$

Hence, the value of x = $\dfrac{1}{4}$.

(iii) Given, 2.5 : 1.5 = x : 3

$\Rightarrow \dfrac{2.5}{1.5} = \dfrac{x}{3} \\[0.5em] \Rightarrow x = \dfrac{2.5}{1.5} \times 3 \\[0.5em] \Rightarrow x = \dfrac{7.5}{1.5} \\[0.5em] \Rightarrow x = 5.$

Hence, the value of x = 5.

(iv) Given, x : 50 :: 3 : 2

$\Rightarrow \dfrac{x}{50} = \dfrac{3}{2} \\[0.5em] \Rightarrow x = \dfrac{3}{2} \times 50 \\[0.5em] \Rightarrow x = \dfrac{150}{2} \\[0.5em] \Rightarrow x = 75.$

Hence, the value of x = 75.