For a long transmission line receiving end voltage is higher than sending end voltage, this indicated Ferranti effect

V_{s} = A V_{R} (at the lightly loaded condition)

Where

V_{s} is the sending end voltage

V_{R} is the receiving end voltage

Also from the ABCD parameters, the approximate value of A is

\(A=1+\frac{YZ}{2}=1-\frac{\omega^{2}l^{2}}{2V^{2}}\)

\( A = \frac{{{V_S}}}{{{V_R}}} = \frac{{400 \times {{10}^3}}}{{420 \times {{10}^3}}} = 0.95\)

\(A=0.95=1 - \frac{{{\omega ^2}{l^2}}}{{2{V^2}}}\)

\(⇒ 1 - \frac{{{{\left( {2\pi \times 50} \right)}^2}{l^2}}}{{2 \times {{\left( {C} \right)}^2}}} = 0.95 \)

⇒ l = 294.8 km

**Therefore the length of the transmission line will be 294.8km**