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

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 b² = ac.

∴ From the definition of continued proportion, we get:

⇒ (16 - x)² = (12 - x)(21 - x)

⇒ 256 + x² – 32x = 252 - 33x + x²

⇒-32x + 33x = 252 – 256

⇒ x= -4

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