Question

If x:y = 1:2 , find 2x+y/y-x​

Answer 1

If x:y = 1:2 , then 2x+y/y-x is 4

Step-by-step explanation:

Given: $x:y= \frac{x}{y} = 1/2$

To be found: $\frac{2x+y}{y-x}$

Since we only have the value of $x/y$ with us, we need to resolve the given expression in terms of $x/y$ by doing some modifications and then substitute the value of $x/y$ (as given) in that simplified expression.

Let us divide the numerator and denominator by $y$,

We have,

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

= $\frac{2(x/y) + 1}{ 1 - x/y}$   ( y and y cancels out )

= $\frac{2*(1/2) + 1}{1- 1/2}$  (Substituting the value of x/y)

= $\frac{1 + 1}{1/2}$

= $\frac{2}{1/2} = 4$

So, if x:y = 1:2 , then 2x+y/y-x is 4