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Verified answer

Question:-

Find the value of x in the following proportion:

i. 25 : x :: 5 : 2

ii. x : 100 :: 3 : 12

iii. 8 : 17.5 :: x : 35

iv. 2 : 9 :: 6 : x

SolutioN:-

[tex] \sf \: i) \: 25 : x :: 5 : 2[/tex]

[tex] \sf \longrightarrow \: 25 : x :: 5 : 2[/tex]

[tex] \sf \longrightarrow \: \frac{25}{x} = \frac{5}{2} \\ [/tex]

[tex] \sf \longrightarrow \: 2 \times 25 = x \times 5[/tex]

[tex] \sf \longrightarrow \: 50= 5x[/tex]

[tex] \sf \longrightarrow \: 5x = 50[/tex]

[tex] \sf \longrightarrow \: x = \frac{50}{5} \\ [/tex]

[tex] \longrightarrow{\underline {\boxed{\sf{ \:x = 10}}}}[/tex]

[tex] \sf \: ii) \: x : 100 :: 3 : 12[/tex]

[tex] \sf \longrightarrow \: x : 100 :: 3 : 12[/tex]

[tex] \sf \longrightarrow \: \frac{x}{100} = \frac{3}{12} \\ [/tex]

[tex] \sf \longrightarrow \: 12 \times x = 3 \times 100 [/tex]

[tex] \sf \longrightarrow \: 12 x = 300[/tex]

[tex] \sf \longrightarrow \: x = \frac{300}{12} \\ [/tex]

[tex] \longrightarrow{\underline {\boxed{\sf{ \:x = 25}}}}[/tex]

[tex] \sf \: iii) \:8 : 17.5 :: x : 35[/tex]

[tex] \sf \longrightarrow \: 8 : 17.5 :: x : 35[/tex]

[tex] \sf \longrightarrow \: \frac{8}{17.5} = \frac{x}{35} \\ [/tex]

[tex] \sf \longrightarrow \: 35 \times 8 = 17.5 \times x [/tex]

[tex] \sf \longrightarrow \: 280 = 17.5 x [/tex]

[tex] \sf \longrightarrow \:17.5 x = 280[/tex]

[tex] \sf \longrightarrow \:x = \frac{280}{17.5} \\ [/tex]

[tex] \longrightarrow{\underline {\boxed{\sf{ \:x = 16}}}}[/tex]

[tex] \sf \: iv) \:2 : 9 :: 6 : x[/tex]

[tex] \sf \longrightarrow \:2 : 9 :: 6 : x[/tex]

[tex] \sf \longrightarrow \: \frac{2}{9} = \frac{6}{x} \\ [/tex]

[tex] \sf \longrightarrow \: 2 \times x = 6 \times 9 [/tex]

[tex] \sf \longrightarrow \: 2 x =54[/tex]

[tex] \sf \longrightarrow \: x = \frac{54}{2} \\ [/tex]

[tex] \longrightarrow{\underline {\boxed{\sf{ \:x = 27}}}}[/tex]