Question : Find 2 numbers such that their mean proportional is 25 and their third proportional is 25.
Option 1: 5 and 5
Option 2: 5 and 25
Option 3: 25 and 125
Option 4: 25 and 25
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Correct Answer: 25 and 25
Solution :
Let, the two numbers be $x$ and $y$, respectively.
The mean proportional between $x$ and $y$ is 25.
$x:25=25:y$
⇒ $xy=625$
The third proportional to $x$ and $y$ is 25.
$x:y=y:25$
⇒ $y^2=25x$
⇒ $y^2=25×\frac{625}{y}$
⇒ $y^3=25×625=15625=25$
$∴y=25$
Now, $x=\frac{625}{y}=25$
So, the two numbers are 25 and 25, respectively.
Hence, the correct answer is 25 and 25.
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