If 2 : 9 :: x : 27, find the value of x.

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Solution

Product of the extremes = 2 $\times$ 27 = 54
Product of the means = 9 $\times$ x = 9x

Since 2 : 9 :: x : 27, we have:
Product of the extremes = Product of the means
⇒ 54 = 9x
⇒ x = 6

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