Question

If $\frac{1}{x}+y=3$ and $x+\frac{1}{y}=2$ then $x:y$ is

• A. $3:2$
• B. $2:3$
• C. $1:2$
• D. $2:1$

Answer 1

Answer: (B)

$2:3$

The question states '...then x: is'

It should state '..then x:y is'

Given

$\frac{1}{x}+y=3$ --- Eqn (1)

$x+\frac{1}{y}=2$ ---Eqn (2)

Multiplying Eqn (1) by x and Eqn (2) by y, we get:

$x(\frac{1}{x}+y)=3x\Rightarrow 1+yx=3x$ --- Eqn (3)

$y(x+\frac{1}{y})=2y\Rightarrow xy+1=2y$ --- Eqn (4)

Subtracting Eqn (4) and Eqn (5), we get:

$1+yx-1-yx=3x-2y$

$\Rightarrow 0=3x-2y$

$\Rightarrow 3x=2y$

$\Rightarrow \frac{x}{y}=\frac{2}{3}$

$\therefore x:y=2:3$

Hence the answer is B