Question

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

Answer 1

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.

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