Question

which number should be subtracted from 12,16,21 so that resultant number are in continued proportion

Answer 1

12-x,16-x,21-x are in same proportion .
(16-x)(16-x)=(21-x)(12-x)
256-32x+x^2=252-34x+x^2
33x-32x=252-256
x= -4

Answer 2

The resultant number will be -4.

Let the number which is to be subtracted from 12 , 16 and 21 be = N

When the resultant numbers will be in a continued proportion, the numbers will be = 12- N, 16 - N  and 21- N

Number will be in proportion when -

= (12-N)/(16-N)  = (16-N)/(21-N)

= (12-N)(21-N) = (16-N)²

= 252 + N² -12N - 21N = 256 + N² - 32N

= -4 = N

Thus, -4 is to be subtracted

Therefore, the resultant numbers will be -

= 12 -(-4) = 16

= 16-(-4) = 20

= 21-(-4) = 25