Question

If $\frac{x}{y}=\frac{c}{d}$ and $\frac{d}{c}=\frac{b}{a}$, which of the following must be true?
I. $\frac{y}{x}=\frac{b}{a}$
II. $\frac{x}{a}=\frac{y}{b}$
III. $\frac{y}{a}=\frac{x}{b}$

• A. I only
• B. II only
• C. I and II only
• D. I and III only
• E. I, II and III

Answer 1

The correct option is C I and II only

$\frac{x}{y}=\frac{c}{d}$ and $\frac{d}{c}=\frac{b}{a}$

$\Rightarrow$ $\frac{x}{y}=\frac{c}{d}=\frac{a}{b}$

Statement III gives ,

$\frac{y}{a}=\frac{x}{b}$$\Rightarrow$ $\frac{b}{a}=\frac{x}{y}$ which is wrong.

So, from the given options,

I and II hold true. So, option C is correct.