#### Answer

10

#### Work Step by Step

It is given that on each correct answer I have paid 8c and on each wrong answer fine is 5c.
Let as suppose that I have done \[X\] problems correctly and have done \[Y\]problems wrong
So, total question I have done
\[X+Y=26\]……(1)
And the money exchanged between us is zero, we can write it in algebraic expression
\[8X-5Y=0\]
\[8X=5Y\]…… (2)
Rewrite equation (1)as follows:
\[X=26-Y\]
Now, substitute this value in the equation (2) and solve for Y.
\[\begin{align}
& 8\left( 26-Y \right)=5Y \\
& 208-8Y=5Y \\
& -13Y=208 \\
& Y=16
\end{align}\]
Now when substitute back the value of Y in equation (1)to obtain,
\[\begin{align}
& X=26-16 \\
& X=10 \\
\end{align}\]
Where X is the number of Questions I have done correctly.
10 problems were solved correctly.