The LCM and HCF of two numbers are 45 and 3 respectively

Answer: (C) 6 

Solution:-
Let the two numbers be a & b

The LCM and HCF of two numbers are 45 and 3, 
Then, the product of two numbers = 45 x 3 
 ab = 135     …………..(1) 

The sum of two numbers  (a + b) = 24
Square on both side, 
(a + b)^2 = 24^2
a^2 + b^2 + 2 ab = 576
a^2 + b^2 = 576 – 2 x 135                  {From equation (1)  ab = 135}
a^2 + b^2 = 576 – 270
 a^2 + b^2 = 306  ………………. (2) 

Difference of two both numbers  = a – b
(a – b)^2  = a^2 + b^2 – 2 ab
From equation (1) ab = 1  &  equation (2)  a^2 + b^2 = 306, 
Then,   (a – b)^2  = 306 – 2 x 135
 (a – b)^2 = 306 – 270
 (a – b)^2 = 36
Square root on both side, 
a – b = 6 

Then, the difference between of two numbers is 6. 

Hence, the correct answer is option (C) 6.