When a number is divided by 3, 4, 6, 15 and 20, the remainder in each case is 1. Also, the number is the greatest 3-digit number. The sum of the digits of the number is:

K(lcm of 3,4,6,15,20) + s , where s is the common remainder (ie 1)
K*60 +1
K=0,1,2,3 and so on.
So when k=16 we get the highest 3 digit no. Ie - 960+1= 961
So sum of digits = 16

You can crack it by taking 980,960 or 940and adding 1 in the end as these values are the only ones that are divisible by 20 in 900 range, its easier just to divide using calc and check

LCM - 60.. Smallest number 60 + 1 = 61....

then add '60' till largest three digit which is 961.. ANS :- 9+6+1 = 16