Question : If $x: y: z=3: 4: 5$, then what will be the ratio of $\left(\frac{x}{y}\right):\left(\frac{y}{z}\right):\left(\frac{z}{x}\right)$?
Option 1: 49 : 37 : 100
Option 2: 45 : 48 : 100
Option 3: 41 : 37 : 100
Option 4: 37 : 47 : 100
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Correct Answer: 45 : 48 : 100
Solution :
Given, $x:y:z=3:4:5$
Let $x=3k, y=4k$ and $z=5k$
So, $\left(\frac{x}{y}\right):\left(\frac{y}{z}\right):\left(\frac{z}{x}\right)$
$=\frac{3k}{4k}:\frac{4k}{5k}:\frac{5k}{3k}$
$=\frac{3}{4}\times 60:\frac{4}{5}\times 60:\frac{5}{3}\times 60$ [$\because$ 60 is LCM of 4, 5, and 3]
$=45:48:100$
Hence, the correct answer is 45 : 48 : 100.
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