Answer :

Let x be the number that should be subtracted from 12, 16, 21 so that the numbers remain in continued proportion.

Numbers a, b, c are said to be continued proportion if b^{2} = ac.

∴ From the definition of continued proportion, we get:

⇒ (16 - x)^{2} = (12 - x)(21 - x)

⇒ 256 + x^{2} – 32x = 252 - 33x + x^{2}

⇒-32x + 33x = 252 – 256

⇒ x= -4

∴ -4 should be subtracted from 12, 16, 21 so that the numbers remain in continued proportion.

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