Efficiency of the transformer, \(\eta=90 \%\)

Input power, \(P_{\mathrm{in}}=3\, \mathrm{kW}=3 \times 10^{3}\, \mathrm{W}=3000\, \mathrm{W}\)

Voltage across the primary coil, \(V_{p}=200\, \mathrm{V}\)

Current in the secondary coil, \(I_{s}=6\, \mathrm{A}\) As \(P_{\text {in }}=I_{p} V_{p}\)

\(\therefore\) Current in the primary coil,

\(I_{p}=\frac{P_{\text {in }}}{V_{p}}=\frac{3000 \mathrm{W}}{200 \mathrm{V}}=15\, \mathrm{A}\)

Efficiency of the transformer,

\(\eta=\frac{P_{\text {out }}}{P_{\text {in }}}=\frac{V_{s} I_{s}}{V_{p} I_{p}}\)

\(\therefore \quad \frac{90}{100}=\frac{6 V_{s}}{3000}\) or \(V_{s}=\frac{90 \times 3000}{100 \times 6}=450\, \mathrm{V}\)