UPSC CDS 1 2018 Math Paper

Since two numbers are greater than 21 and also their H.C.F. is 21
∴ Two numbers are 21a and 21b, where a > 1, b > 1 and a, b are co-prime.
Now,
21a×21b=3003×21
a×b=143
As, a and b are co-primes. So, a = 11 and b = 13
∴ Sum of numbers
=21(11+13)
=21×24=504