If the sum of the roots of the quadratic equation $ky^2 - 11y + (k - 23) = 0$ is $\frac{13}{21}$ more than the product of the roots, then find the value of $k$.

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Step 1: $ky^2 - 11y + (k - 23) = 0$. Here $a = k$, $b = -11$, $c = k - 23$
Sum of roots $= \frac{11}{k}$
Product of roots $= \frac{k - 23}{k}$
Step 2: ATQ: $\frac{11}{k} - \frac{k - 23}{k} = \frac{13}{21}$
Step 3: Solving, we get $k = 21$

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