There are two numbers which are greater than 21 and their LCM and HCF are 3003 and 21 respectively. What is the sum of these numbers?

We are given that the HCF of two numbers is 21. Let the numbers be X, and Y. Then X and Y can be written as,

X = 21a and Y = 21b where a and b are coprimes.

We know that, 

product of the numbers =  LCM * HCF

X * Y = 3003 * 21

21a * 21b = 3003 * 21

a * b = 143

a * b = 11 * 13

There are two possibilities for (a,b) with a and b as coprimes, one being (1, 143) and the other being (11, 13). We cannot take (1, 143) because, in this case, one of the numbers would be 21, but we are given that both numbers are greater than 21. So, the numbers X and Y are 21 * 11 and 21 * 13, which are 231 and 273. So, the sum of the numbers = 231 + 273 = 504.

Therefore, the correct answer is option A.