Question

if A/2=B/3=C/4 then A:B:C=?

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{\dfrac{A}{2}=\dfrac{B}{3}=\dfrac{C}{4}}$

$\underline{\textsf{To find:}}$

$\mathsf{A:B:C}$

$\underline{\textsf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{A}{2}=\dfrac{B}{3}=\dfrac{C}{4}=k\;(say)}$

$\implies\mathsf{\dfrac{A}{2}=k\;\;|\;\;\dfrac{B}{3}=k\;\;|\;\;\dfrac{C}{4}=k}$

$\implies\mathsf{A=2k\;\;|\;\;B=3k\;\;|\;\;C=4k}$

$\mathsf{Now,}$

$\mathsf{A:B:C}$

$\mathsf{=2k:3k:4k}$

$\textsf{Divide through out by k}$

$\mathsf{=2:3:4}$

$\implies\boxed{\mathsf{A:B:C=2:3:4}}$

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Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ \frac{ A}{2} =\frac{ B}{3} = \frac{ C}{4}}$

TO DETERMINE

A : B : C

EVALUATION

Here it is given that

$\displaystyle \sf{ \frac{ A}{2} =\frac{ B}{3} = \frac{ C}{4}}$

Here the denominators are 2 , 3 , 4

LCM of the denominators = 12

Multiplying each fractions by 12 we get

$\displaystyle \sf{ \frac{ A}{2} \times 12 =\frac{ B}{3} \times 12 = \frac{ C}{4} \times 12}$

$\implies \: \displaystyle \sf{ 6{ A}=4{ B} = 3{ C}}$

$\implies \: \displaystyle \sf{ A = \frac{ 3 C\: }{6} \: \: \: and \: \: \: \: B = \frac{ 3 C\: }{4} }$

$\therefore \sf{ \: \: A : B : C \: }$

$= \displaystyle \sf{ \frac{ 3 C\: }{6} : \frac{ 3 C\: }{4} : C}$

$= \displaystyle \sf{ \frac{ 1}{2} : \frac{ 3 \: }{4} : 1}$

$= \displaystyle \sf{ 2 : 3 : 4}$

FINAL ANSWER

$\boxed{ \: \sf{ \: \: A : B : C \: } = \: 2 : 3 : 4 \: \: }$

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