Question

A:B = 2:3 , B:C = 4:5 , C:D = 6:7 Then A:D = ?​

Answer 1

$ad = 8 :9 \\ ..$

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

$\rm \: A : B \: = \: 2 : 3$

$\rm\implies \:\dfrac{A}{B} = \dfrac{2}{3} - - - (1)$

Also,

$\rm \: B : C \: = \: 4 : 5$

$\rm\implies \:\dfrac{B}{C} = \dfrac{4}{5} - - - (2)$

Also,

$\rm \: C : D \: = \: 6 : 7$

$\rm\implies \:\dfrac{C}{D} = \dfrac{6}{7} - - - (3)$

Now, on multiply equation (1), (2) and (3), we get

$\rm \: \dfrac{A}{B} \times \dfrac{B}{C} \times \dfrac{C}{D} = \dfrac{2}{3} \times \dfrac{4}{5} \times \dfrac{6}{7}$

$\rm \: \dfrac{A}{D} = \dfrac{16}{35}$

$\rm\implies \:A : D \: = \: 16 : 35$

$\rule{190pt}{2pt}$

Additional Information :-

1. If a : b : : c : d, then

$\boxed{\rm{  \: \frac{a}{c} = \frac{b}{d} \: is \: called \: alternendo \: }}$

$\boxed{\rm{  \: \frac{b}{a} = \frac{d}{c} \: is \: called \: invertendo \: }}$

$\boxed{\rm{ \:\dfrac{a + b}{b} = \dfrac{c + d}{d} \: is \: called \: componendo \: }}$

$\boxed{\rm{ \:\dfrac{a - b}{b} = \dfrac{c-d}{d} \: is \: called \: dividendo \: }}$

$\boxed{\rm{ \:\dfrac{a - b}{a + b} = \dfrac{c-d}{c + d} \: is \: called \: componendo \: and \: dividendo \: }}$