Explanation:

Approach I:
Let the Numbers be 5x, 6x and 7x
∴   (5x)² + (6x)² + (7x)² = 990
⇒  25x² + 36x² + 49x² = 990
⇒  110x² = 990
⇒  x² = 9
⇒  x = 3
∴  Numbers = 15, 18 and 21.
Approach II:  Pick each of the options. Add unit digits of the squares of unit digit of the numbers given in a particular option and match the resultant unit digit with the unit digit of the given total;
0 in 990.
Squares of the unit digits of the numbers (15, 18, 21) given in option C are 5, 4 and 1 which on addition give us 10 the unit digit of which is 0.