Question 2520
Suppose that total problem solved correctly be x and that done incorrectly be y

as total 26 problems are done
x+y = 26 ...........Equation(1)

.08 cents is paid for each right answer
so for x correct answers total amount paid will be .08x

.05 cents are fined for each incorrect answer
so for y incorrect answers total amount fined will be .05y

Now at the end of 26 problems no money is owed by neone...this means the amount to be paid and to be fined are equal
=> .08x = .05y
=> .08x -.05y = 0
=> (8/100)x - (5/100)y = 0
=> (8x-5y)/100 = 0
=> 8x-5y = 0
=> 8x = 5y
=> x = 5y/8............equation(2)
substituting the value of x from equation(2) to equation(1)
x+y = 26
=> 5y/8 + y = 26
=> 13y/8 = 26
=> 13y = 26*8
=> y = 16
so x= 10

No. of problems done right is 10