Question

If $\frac{y}{x-z}=\frac{y+x}{z}=\frac{x}{y}$ then find $x:y:z$

• A. $1:2:3$
• B. $3:2:1$
• C. $4:2:3$
• D. $2:4:7$

Answer 1

The correct option is C $4:2:3$

$\frac{y}{x-z}=\frac{y+x}{z}=\frac{x}{y}$

Now,

$\frac{y}{x-z}=\frac{x}{y}$

$y^2=x^2-xz......\left(1\right)$

And

$\frac{y+x}{z}=\frac{x}{y}$

$y^2+xy=xz......\left(2\right)$

$x^2-xz+xy=xz$

$x-z+y=z$

$2z=x+y......\left(3\right)$

$And$

$\frac{y}{x-z}=\frac{y+x}{z}$

$yz=xy-yz+x^2-xz$

$2yz=xy+x^2-xz$

$2yz=x(y+x)-xz$ [From equation (3)]

$2yz=2xz-xz$

$2yz=xz$

$2y=x$

$\frac{x}{y}=\frac{2}{1}......\left(4\right)$

Substituting this value in equation (3), we get

$2z=2y+y$

$2z=3y$

$\frac{y}{z}=\frac{2}{3}......\left(5\right)$

By equation (4) and (5), we get

$x:y:z=4:2:3.$

Hence, this is the answer.