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Question Number 104452 by Anindita last updated on 21/Jul/20

If A:B = 3:4, B:C = 6:7 then A:B:C = ? A:C = ?

$$\mathrm{If}\:\mathrm{A}:\mathrm{B}\:=\:\mathrm{3}:\mathrm{4},\:\mathrm{B}:\mathrm{C}\:=\:\mathrm{6}:\mathrm{7}\:\mathrm{then} \\ $$$$\mathrm{A}:\mathrm{B}:\mathrm{C}\:=\:?\:\mathrm{A}:\mathrm{C}\:=\:?\: \\ $$

Answered by bemath last updated on 21/Jul/20

A : B : C = 9 : 12 : 14

$${A}\::\:{B}\::\:{C}\:=\:\mathrm{9}\::\:\mathrm{12}\::\:\mathrm{14} \\ $$

Answered by Rasheed.Sindhi last updated on 22/Jul/20

determinant ((( A),( :),( B),:,( C)),(( 3),( :),( 4),,),(,,( 6),:,( 7)),((−−),−,(−−−−),−,(−−)),((3×3_(−) ),,( 4×3_(−) ),,),(,,(=6×2_(−) ),,(7×2_(−) )),((−−),−,(−−−−),−,(−−)),(9,( :),(12_(lcm of 4 & 6) ),( :),( 14))) A:C=9:14

$$\begin{vmatrix}{\:\:\mathrm{A}}&{\:\:\::}&{\:\:\:\:\:\:\:\:\:\mathrm{B}}&{:}&{\:\:\mathrm{C}}\\{\:\:\mathrm{3}}&{\:\:\::}&{\:\:\:\:\:\:\:\:\:\mathrm{4}}&{}&{}\\{}&{}&{\:\:\:\:\:\:\:\:\:\mathrm{6}}&{:}&{\:\:\:\mathrm{7}}\\{−−}&{−}&{−−−−}&{−}&{−−}\\{\mathrm{3}×\underset{−} {\mathrm{3}}}&{}&{\:\:\:\mathrm{4}×\underset{−} {\mathrm{3}}}&{}&{}\\{}&{}&{=\mathrm{6}×\underset{−} {\mathrm{2}}}&{}&{\mathrm{7}×\underset{−} {\mathrm{2}}}\\{−−}&{−}&{−−−−}&{−}&{−−}\\{\mathrm{9}}&{\:\::}&{\underset{{lcm}\:{of}\:\mathrm{4}\:\&\:\mathrm{6}} {\mathrm{12}}}&{\:\::}&{\:\:\:\:\:\mathrm{14}}\end{vmatrix} \\ $$$$\mathrm{A}:\mathrm{C}=\mathrm{9}:\mathrm{14} \\ $$

Commented by harckinwunmy last updated on 21/Jul/20

can u pls explain

$$\mathrm{can}\:\mathrm{u}\:\mathrm{pls}\:\mathrm{explain} \\ $$

Commented by Rasheed.Sindhi last updated on 22/Jul/20

Try to understand now please.

$$\mathcal{T}{ry}\:{to}\:{understand}\:{now}\:{please}. \\ $$

Answered by 1549442205PVT last updated on 22/Jul/20

From the hypothesis we get (A/3)=(B/4),(B/6)=(C/7)⇒B=((6C)/7)=(C/(7/6))⇒(B/4)=(C/((7/6)×4)) ⇒(A/3)=(B/4)=(C/((14)/3))⇒A:B:C=3:4:((14)/3)=9:12:14 A:C=3:((14)/3)=9:14

$$\mathrm{From}\:\mathrm{the}\:\mathrm{hypothesis}\:\mathrm{we}\:\mathrm{get} \\ $$$$\frac{\mathrm{A}}{\mathrm{3}}=\frac{\mathrm{B}}{\mathrm{4}},\frac{\mathrm{B}}{\mathrm{6}}=\frac{\mathrm{C}}{\mathrm{7}}\Rightarrow\mathrm{B}=\frac{\mathrm{6C}}{\mathrm{7}}=\frac{\mathrm{C}}{\frac{\mathrm{7}}{\mathrm{6}}}\Rightarrow\frac{\mathrm{B}}{\mathrm{4}}=\frac{\mathrm{C}}{\frac{\mathrm{7}}{\mathrm{6}}×\mathrm{4}} \\ $$$$\Rightarrow\frac{\boldsymbol{\mathrm{A}}}{\mathrm{3}}=\frac{\boldsymbol{\mathrm{B}}}{\mathrm{4}}=\frac{\boldsymbol{\mathrm{C}}}{\frac{\mathrm{14}}{\mathrm{3}}}\Rightarrow\boldsymbol{\mathrm{A}}:\boldsymbol{\mathrm{B}}:\boldsymbol{\mathrm{C}}=\mathrm{3}:\mathrm{4}:\frac{\mathrm{14}}{\mathrm{3}}=\mathrm{9}:\mathrm{12}:\mathrm{14} \\ $$$$\boldsymbol{\mathrm{A}}:\boldsymbol{\mathrm{C}}=\mathrm{3}:\frac{\mathrm{14}}{\mathrm{3}}=\mathrm{9}:\mathrm{14} \\ $$

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