KnowledgeBoat Logo
|

Mathematics

If 7a−4b7c−4d=7a+4b7c+4d\dfrac{7a - 4b}{7c - 4d} = \dfrac{7a + 4b}{7c + 4d}, then b : a is :

  1. c : d

  2. d : c

  3. 7a : 4b

  4. 7c : 4d

Ratio Proportion

3 Likes

Answer

Given,

⇒7a−4b7c−4d=7a+4b7c+4d\Rightarrow \dfrac{7a - 4b}{7c - 4d} = \dfrac{7a + 4b}{7c + 4d}

Applying alternendo,

⇒7a−4b7a+4b=7c−4d7c+4d\Rightarrow \dfrac{7a - 4b}{7a + 4b} = \dfrac{7c - 4d}{7c + 4d}

Applying componendo and dividendo we get :

⇒7a−4b+7a+4b7a−4b−(7a+4b)=7c−4d+7c+4d7c−4d−(7c+4d)⇒14a7a−7a−4b−4b=14c7c−7c−4d−4d⇒14a−8b=14c−8d⇒−14a8b=−14c8d⇒ab=cd⇒ba=dc.\Rightarrow \dfrac{7a - 4b + 7a + 4b}{7a - 4b - (7a + 4b)} = \dfrac{7c - 4d + 7c + 4d}{7c - 4d - (7c + 4d)} \\[1em] \Rightarrow \dfrac{14a}{7a - 7a - 4b - 4b} = \dfrac{14c}{7c - 7c - 4d - 4d} \\[1em] \Rightarrow \dfrac{14a}{-8b} = \dfrac{14c}{-8d} \\[1em] \Rightarrow -\dfrac{14a}{8b} = -\dfrac{14c}{8d} \\[1em] \Rightarrow \dfrac{a}{b} = \dfrac{c}{d} \\[1em] \Rightarrow \dfrac{b}{a} = \dfrac{d}{c}.

Hence, Option 2 is the correct option.

Answered By

1 Like

Related Questions