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**Hint:**For solving this particular problem we must use the given statement that is $yz:zx:xy = 1:2:3$ then separate this ratio into two parts one is $yz:zx = 1:2$ to get the ratio of $y:x = 1:2$ and other is $zx:xy = 2:3$ to get the ratio of $z:y = 2:3$ . then after evaluating the result we get our desired result.

**Complete solution step by step:**

It is given that ,

$yz:zx:xy = 1:2:3$ (given)

Or

$yz:zx = 1:2$

Now consider the following equation as our first equation,

$y:x = 1:2.........(1)$

And

$zx:xy = 2:3$

Now consider the following equation as our second equation,

$z:y = 2:3................(2)$

Now multiply equation one by three and equate it with the second equation . we will get ,

$x:y:z = 6:3:2$

Now we have to find $\dfrac{x}{{yz}}:\dfrac{y}{{zx}}$ ,

$ \Rightarrow \dfrac{x}{{yz}}:\dfrac{y}{{zx}} = \dfrac{6}{1}:\dfrac{3}{2}$ ,

After simplification we will get ,

$

\Rightarrow \dfrac{x}{{yz}}:\dfrac{y}{{zx}} = \dfrac{2}{1}:\dfrac{1}{2} \\

\\

$

$ = 4:1$

Hence we get our required result that is $4:1$ .

**Therefore, we can say that option D is the correct one.**

**Additional Information :**A ratio is comparison of values of two quantities of the identical type and having the same unit by division.

Ratio of two quantities a and b is that the fraction ba and that we write it as a:b.

Example:,

If two girls and five boys were born on a specific day in an exceedingly hospital.

We can write the ratio of the number of ladies to boys as 2:5 or 52.

The ratio of the number of boys to girls is written as 5:2 or 25 .

**Note:**Ratio could be a fraction.

• Ratio does not have a unit.

• Units of both the quantities involved during a ratio must be the same.

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