The ideal transformer (either step-up or step-down) works with the equation:
$\frac{V_s}{V_p}=\frac{N_s}{N_p}=\frac{I_p}{I_s}$
where $V_s$ and $V_p$ are the voltages applied to the secondary and the primary respectively
$N_s$ and $N_p$ are the number of turns on the secondary and primary coils respectively
$I_p$ and $I_s$ are the currents flowing in the primary and secondary coils respectively.
$\frac{V_s}{100}=\frac{200}{100}$
$V_s=\frac{200\times 100}{100}=200V$