a+b=29

a+c=25

b+c=20

The solution is a= 17b= 12c=8.

The total score is17 * 20+(12+8) * 25 = 840.

According to "each student answered at least one question correctly, one person answered all three questions correctly, and 15 people answered two questions correctly"

You can count the number of people.

A+B+C = 37. (Among 37 people, 3 questions are correctly counted twice, and 2 questions are correctly counted 1 time. )

So 37-2 *1-1*15 = 20 people.

So the average score is 840/20=42 points.