Find two numbers such that their mean proportional is 18 and the third proportional to them is 144.

Let the numbers are x and y,

Mean proportional = √xy = 18

⇒ xy = 324      ---- (1)

Third proportional = y²/x = 144

⇒ y² = 144x     ---- (2)

Putting the value of x from this in 1^st equation,

⇒ y³/144 = 324

⇒ y³ = 324 × 144

⇒ y³ = 18 × 18 × 18 × 8

⇒ y = 18 × 2

⇒ y = 36 and x = 324/36 = 9

Hi friends, it's answer is 9 and 36. Surely!!!!

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