Question

If 13A = 11B = 8C, find A : B : C

A) 143:104:88 B) 104:88:143 C) 88:104:143 D) 8:11:13

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume that, 13A = 11B = 8C = k , (where k is any constant integer .)

Than,

→ 13A = k

→ A = (k/13)

Similarly,

→ 11B = k

→ B = (k/11)

And,

→ 8C = k

→ C = (k/8)

So,

→ A : B : C = (k/13) : (k/11) : (k/8)

→ A : B : C = { 11*8*k : 13*8*k : 13*11*k } /(13 * 11 * 8)

→ A : B : C = { 88k : 104k : 143k } / (13 * 11 * 8)

→ A : B : C = { 88 : 104 : 143 } / (13 * 11 * 8)

→ A : B : C = 88 : 104 : 143 (C) (Ans.)

Answer 2

${ \bold{ \huge{ \underline{ \underline{ \red{Question:-}}}}}}$



▪ If 13 A = 11 B = 8 C

Find A : B : C



${ \bold{ \huge{ \underline{ \underline{ \red{Solution:-}}}}}}$



▪ Let 13 A = 11 B = 8 C = k


( where, k is a constant)


✮ 13 A = K



${ \boxed{ \bold{ \implies{ \pink{A = \frac{K}{13}}}}}}$



✮ 11 B = K




${ \boxed{ \bold{ \implies{ \pink{B = \frac{K}{11}}}}}}$




✮ 8 C = K




${ \boxed{ \bold{ \implies{ \pink{C = \frac{K }{8}}}}}}$



thus,



➟ A : B : C = K/13 : K/11 : K/8





➟ A : B : C = ( 11×8 K : 13×8 K : 13×11 k )/13×11×8





➟ A : B : C = ( 88 K : 104 K : 143 K)/13×11×8






➟ A : B : C = ( 88 : 104 : 143 ) / 13×11×8





➟ A : B : C = 88 : 104 : 143




therefore, option c) is correct