Question

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

Answer 1

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

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

∴ `(12 − x)/(16 − x) = (16 − x)/(21 − x)`

∴ `((12 − x) - (16 - x))/(16 - x) = ((16 - x) - (21 - x))/(21 - x)`  ...(Using Dividendo)

∴ `(12 - x - 16 + x)/(16 - x) = (16 - x - 21 + x)/(21 - x)` 

∴ `(-4)/(16 - x) = (-5)/(21 - x)`

∴ −4 (21 − x) = −5 (16 − x)

∴ −84 + 4x = −80 + 5x

∴ −84 + 80 = 5x − 4x

∴ −4 = x

∴ x = −4

Thus, the number −4 must be subtracted from 12, 16 and 21 so that the resultant numbers are in continued proportion.