correct answer is: d) 984

Explanation

3 digits greatest number is 999 .
5 digits greatest number is 99999 .
If we subtract 999 from 99999 , we get:
\left(99999-999\right)
\rightarrow 99000
Now, if we divide 99000 by 123 then we get,
\left(99000\div123\right)
\rightarrow 804 is quotient and 108 is remainder.
Since we want a remainder of '0' so we need to subtract the remainder (108) from the divisor (123) .
\left(123-108\right)
\rightarrow 15
Now, we need to add 15 to 99000 so that we get the 5 digits number which is completely divisible by 123 .
\therefore\left(99000+15\right)
\rightarrow 99015
\therefore 99015 is the 5 digits number that is completely divisible by 123 .
And if we subtract 99015 from 5 digits greatest number 99999 then we get the 3 digits greatest number which must be subtract.
\therefore\left(99999-99015\right)
\rightarrow 984
So that, 984 is the greatest number of 3 digits which can be subtracted from the greatest number of 5 digits, so that the remainder may be exactly divisible by 123.
Ans: The greatest 3 digit number that can be subtracted from the greatest 5 digit number such that the remainder is exactly divisible by 123 is 984.

Another method to articulate this particular query is available:

1. What is the largest 3-digit number that can be subtracted from the largest 5-digit number to get a remainder divisible by 123?
2. Finding the greatest 3-digit number that, when subtracted from the greatest 5-digit number, leaves a remainder divisible by 123.
3. What is the largest subtraction that can be made from a 5-digit number by a 3-digit number to result in a remainder divisible by 123?