Question

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

Answer 1

Answer:

- 4 is to be subtracted

Step-by-step explanation:

Let say N to be subtracted from 12 , 16 & 21

so that resultant numbers are in continued proportion

then Numbers are

12- N   , 16 - N  & 21- N

Number are in proportion if

(12-N)/(16-N)  = (16-N)/(21-N)

=> (12-N)(21-N) = (16-N)²

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

=> -4 = N

=> -4 is to be subtracted

12 -(-4) = 16

16-(-4) = 20

21-(-4) = 25

Answer 2

Answer:

-4 must be subtracted

Step-by-step explanation:

Let the number x to be subtracted from each of the given numbers.

Then the numbers will be (12 - x), (16 - x) and (21 - x) are in continued proportion.

=> (12 - x)/(16 - x) = (16 - x)/(21 - x)

=> (12 - x)(21 - x) = (16 - x)²

=> 252 - 12x - 21x + x² = 256 - 32x + x²

=> -12x - 21x + 32x = 256 - 252

=> -x = 4

=> x = -4

Hence, -4 should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion.

Hope it helps :)