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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