A few questions/potential problems:
1. Are you giving +1 or +2 points for a correct answer. +2 would mean a max score of 40, not 20. Adjust your divisor as necessary.
2. grades = ((score/20)*100); is integer division. Unless the score is greater than 20, (score/20) will return zero. Either multiply by 100 first, then divide by 20 (should be equivalent to multiply by 5 actually), or cast your score to a float before all this, like so (((float) score)/20)*100.
Also, your if-else is generally fine, but you could simplify, like so
Code:
if (grade < 60) {
printf("F\n");
}
else if (grade < 70) { // the first clause guarantees that, if we get here, grade >= 60
}
else if (grade < 80) { // again, here we're guaranteed grade >= 70
}
...