If $5a + 4b + 20c = t$, then the value of t for which the line $ax + by + c –1 = 0$ always passes through a fixed point is

Equation of line $\frac{ax}{c-1}+\frac{by}{c-1}+1=0$ has two independent parameters.
It can pass through a fixed point if it contains only one independent parameter.
Now there must be one relation between $\frac{a}{c-1}$ and $\frac{b}{c-1}$ independent of a, b and c so that $\frac{a}{c-1}$ can be
expressed in terms of $\frac{b}{c-1}$ and straight line contains only one independent parameter.

Now that given relation can be expressed as $\frac{5a}{c-1}+\frac{4b}{c-1}=\frac{t-20c}{c-1}$

RHS is independent of c if t = 20.