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If A : B : C = 2 : 3 : 4, then ratio ^A/_B : ^B/_C : ^C/_A is equal to?

18 : 9 : 16
28 : 9 : 12
38 : 9 : 24
44 : 9 : 12

Answer:- 1

Explanation:-

Solution:

\begin{aligned} A : B : C = 2 : 3 : 4 \\ Let \\ A = 2 x, B = 3 x, C = 4 x \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} = \frac{2 x}{3 x} : \frac{3 x}{4 x} : \frac{4 x}{2 x} \\ \Rightarrow \frac{2}{3} : \frac{3}{4} : \frac{2}{1} \end{aligned}

$\eqalign{ & {\text{A}}:{\text{B}}:{\text{C}} = 2:3:4 \cr & {\text{Let }} \cr & {\text{A}} = 2x,{\text{B}} = 3x,{\text{C}} = 4x \cr & \therefore \frac{{\text{A}}}{{\text{B}}}:\frac{{\text{B}}}{{\text{C}}}:\frac{{\text{C}}}{{\text{A}}} = \frac{{2x}}{{3x}}:\frac{{3x}}{{4x}}:\frac{{4x}}{{2x}} \cr & \Rightarrow \frac{2}{3}:\frac{3}{4}:\frac{2}{1} \cr}$ Multiply by the L.C.M of denominator to remove fraction

\begin{aligned} So, \\ L .C .M of (3, 4, 1) = 12 \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} \\ \frac{2}{3} \times 12 : \frac{3}{4} \times 12 : \frac{2}{1} \times 12 \\ 8 : 9 : 24 \end{aligned}

$\eqalign{ & {\text{So,}} \cr & {\text{L}}{\text{.C}}{\text{.M of }}\left( {3,4,1} \right) = 12 \cr & \therefore \frac{{\text{A}}}{{\text{B}}}\,\,\,\,\,:\,\,\,\,\,\frac{{\text{B}}}{{\text{C}}}\,\,\,\,\,\,:\,\,\,\,\,\frac{{\text{C}}}{{\text{A}}} \cr & \frac{2}{3} \times 12:\frac{3}{4} \times 12:\frac{2}{1} \times 12 \cr & \,\,\,\,\,\,\,8\,\,\,\,\,\,\,:\,\,\,\,\,\,\,9\,\,\,\,\,\,\,:\,\,\,\,\,\,\,24 \cr}$

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Multiply by the L.C.M of denominator to remove fraction

\begin{aligned} So, \\ L .C .M of (3, 4, 1) = 12 \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} \\ \frac{2}{3} \times 12 : \frac{3}{4} \times 12 : \frac{2}{1} \times 12 \\ 8 : 9 : 24 \end{aligned}

$\eqalign{ & {\text{So,}} \cr & {\text{L}}{\text{.C}}{\text{.M of }}\left( {3,4,1} \right) = 12 \cr & \therefore \frac{{\text{A}}}{{\text{B}}}\,\,\,\,\,:\,\,\,\,\,\frac{{\text{B}}}{{\text{C}}}\,\,\,\,\,\,:\,\,\,\,\,\frac{{\text{C}}}{{\text{A}}} \cr & \frac{2}{3} \times 12:\frac{3}{4} \times 12:\frac{2}{1} \times 12 \cr & \,\,\,\,\,\,\,8\,\,\,\,\,\,\,:\,\,\,\,\,\,\,9\,\,\,\,\,\,\,:\,\,\,\,\,\,\,24 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} A : B : C = 2 : 3 : 4 \\ Let \\ A = 2 x, B = 3 x, C = 4 x \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} = \frac{2 x}{3 x} : \frac{3 x}{4 x} : \frac{4 x}{2 x} \\ \Rightarrow \frac{2}{3} : \frac{3}{4} : \frac{2}{1} \end{aligned}

$\eqalign{ & {\text{A}}:{\text{B}}:{\text{C}} = 2:3:4 \cr & {\text{Let }} \cr & {\text{A}} = 2x,{\text{B}} = 3x,{\text{C}} = 4x \cr & \therefore \frac{{\text{A}}}{{\text{B}}}:\frac{{\text{B}}}{{\text{C}}}:\frac{{\text{C}}}{{\text{A}}} = \frac{{2x}}{{3x}}:\frac{{3x}}{{4x}}:\frac{{4x}}{{2x}} \cr & \Rightarrow \frac{2}{3}:\frac{3}{4}:\frac{2}{1} \cr}$ Multiply by the L.C.M of denominator to remove fraction

\begin{aligned} So, \\ L .C .M of (3, 4, 1) = 12 \\ ∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} \\ \frac{2}{3} \times 12 : \frac{3}{4} \times 12 : \frac{2}{1} \times 12 \\ 8 : 9 : 24 \end{aligned}

$\eqalign{ & {\text{So,}} \cr & {\text{L}}{\text{.C}}{\text{.M of }}\left( {3,4,1} \right) = 12 \cr & \therefore \frac{{\text{A}}}{{\text{B}}}\,\,\,\,\,:\,\,\,\,\,\frac{{\text{B}}}{{\text{C}}}\,\,\,\,\,\,:\,\,\,\,\,\frac{{\text{C}}}{{\text{A}}} \cr & \frac{2}{3} \times 12:\frac{3}{4} \times 12:\frac{2}{1} \times 12 \cr & \,\,\,\,\,\,\,8\,\,\,\,\,\,\,:\,\,\,\,\,\,\,9\,\,\,\,\,\,\,:\,\,\,\,\,\,\,24 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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