Question : If 18, $x$, and 50 are continued proportions, then the value of $x$ is:
Option 1: 30
Option 2: 3
Option 3: 5
Option 4: 32
Correct Answer: 30
Solution : Given: 18, $x$ and 50 are continued proportions. Since, 18, $x$ and 50 are continued proportions, i.e., $18:x::x:50$ ⇒ $\frac{18}{x}=\frac{x}{50}$ ⇒ $x^2=18×50$ ⇒ $x=\sqrt{900}$ $\therefore x=30$ Hence, the correct answer is 30.
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