Three numbers are in the ratio. $$\frac{1}{2}:\frac{2}{3}:\frac{3}{4}.$$   If the difference between the greatest number and the smallest number is 33, the HCF of the three numbers is:

A. 5

B. 9

C. 11

D. 13

Answer: Option C

Solution(By Examveda Team)

Three numbers $$ = \left( {\frac{1}{2}:\frac{2}{3}:\frac{3}{4}} \right) \times 12$$
I : II : III = 6 : 8 : 9
Difference between largest and smallest number is 33
9x - 6x = 33
3x = 33
x = 11
I : II : III = 6 × 11 : 8 × 11 : 9 × 11 = 66 : 88 : 99
HCF of three numbers [66, 88, 99] = 11