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If $yz:zx:xy = 1:2:3$ , then $\dfrac{x}{{yz}}:\dfrac{y}{{zx}}$ is equal to
A. 3:2
B. 1:4
C. 2:1
D. 4:1

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Last updated date: 20th Jun 2024
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Answer
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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.