What is the smallest positive number that should be subtracted from each of 12 and 21 so that 36 is the third proportion to them?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 3.
Calculations:
Let the number be a, b, and c
The numbers are in proportion = a/b = b/c
⇒ (12 - x)/(21 - x) = (21 - x)/36
⇒ (12 - x) × 36 = (21 - x) × (21 - x)
⇒ 432 - 36x = 441 - 21x - 21x + x2
⇒ 432 - 36x = 441 - 42x + x2
⇒ x2 - 6x + 9 = 0
⇒ x2 - 3x - 3x + 9 = 0
⇒ x(x - 3) - 3(x - 3) = 0
⇒ (x - 3)(x - 3) = 0
⇒ x = 3