Question : Find the third proportional to 23 and 31.
Option 1: $\frac{31}{23}$
Option 2: $\frac{961}{23}$
Option 3: $\frac{23}{31}$
Option 4: $\frac{23}{961}$
Correct Answer: $\frac{961}{23}$
Solution : Let the third proportional to 23 and 31 be $x$. $23 : 31:: 31: x$ ⇒ $\frac{23}{31}=\frac{31}{x}$ ⇒ $x=\frac{31\times 31}{23}$ ⇒ $x=\frac{961}{23}$ Hence, the correct answer is $\frac{961}{23}$.
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