Question

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

Continued proportions?​

Answer 1

Answer:

12 , 16 , 21

b2 = a x c

let the x to be subtracted

12-x , 16-x , 21-x

(16-x)2 = (12-x) (21-x)

12 + x / 16 + x = 16 + x / 21 + x

(21+x) ( 21+x) = (16+x) (16+x)

252 + 12x +21x + X2 = 256 +16x +16x + X2

252 + 33x = 256 + 32x

32x - 32x = 256 - 252

x= 5

Answer 2

Answer:

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