Find the value of $x$ in the following proportions:

$(i)7:15::x:30$

$(ii)x:3::12:18$

$(iii)30:x::45:24$

$(iv)8:16::25:x$

If $a:b::c:d$ then $a\times d=b\times c$

$(i).~7:15::x:30$

$\Rightarrow 7\times 30=15 \times x$

$\Rightarrow \dfrac{7 \times 30}{15}=x$

$\Rightarrow 7 \times 2=x$

$\Rightarrow x=14$

$(ii).~x:3::12:18$

$\Rightarrow x\times 18=3 \times 12$

$\Rightarrow x = \dfrac{12 \times 3}{18}$

$\Rightarrow x =2$

$(iii).~30:x::45:24$

$\Rightarrow 30\times 24=x \times 45$

$\Rightarrow \dfrac{30 \times 24}{45}=x$

$\Rightarrow \dfrac{2 \times 24}{3}=x$

$\Rightarrow 16 =x$

$(iv).~8:16::25:x$

$\Rightarrow x\times 8=16 \times 25$

$\Rightarrow x = \dfrac{25 \times 16}{8}$

$\Rightarrow x =25 \times 2$

$\Rightarrow x =50$