Question

A:B=3:4 and B:C=6:11

Answer 1

A : B = 3 : 4

$\frac{A}{B}$ = $\frac{3}{4}$

⇒ A = $\frac{3B}{4}$  

B : C = 6 : 11

$\frac{B}{C}$ = $\frac{6}{11}$

⇒ C = $\frac{11B}{6}$

Now,

(A : B) X (B : C) = (3 : 4) X (6 : 11)

$\frac{A}{B}$ X $\frac{B}{C}$ = $\frac{3}{4}$ X $\frac{6}{11}$

after cancelling .. we get,

$\frac{A}{C} = \frac{3}{2}$ X $\frac{3}{11}$

⇒ $\frac{A}{C} = \frac{9}{22}$ ----------------------> 1

to find A:B:C

we got the value of A to be = $\frac{3B}{4}$

and C = $\frac{11B}{6}$

B = B

A : B : C = $\frac{3B}{4}$ ÷ B ÷ $\frac{11B}{6}$

A : B : C = $\frac{11B}{8}$ --------------------------> 2

from 1 :

$\frac{A}{C} = \frac{9}{22}$

in 2 :

A : B : C = A : C : B

⇒ $(\frac{9}{22}) : B$ = $\frac{11B}{8}$

$\frac{9}{22}$ X $\frac{1}{B}$ = $\frac{11B}{8}$

= 242B² = 72

⇒ A : B : C = $\frac{72}{242B^{2} }$

gosh im getting a complex answr ..