Which number should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion?

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Solution

Le the number x be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion.

∴ (12 − x), (16 − x), (21 − x) are in continued proportion.

$\Rightarrow \frac{12 - x}{16 - x} = \frac{16 - x}{21 - x} \Rightarrow {(16 - x)}^{2} = (12 - x) \times (21 - x) \Rightarrow 256 + x^{2} - 32 x = 252 - 12 x - 21 x + x^{2} \Rightarrow 256 - 32 x = 252 - 33 x \Rightarrow 33 x - 32 x = 252 - 256 \Rightarrow x = - 4$
Thus, the number −4 must be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion.

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