The electron concentration in an n-type semiconductor is the same as hole concentration in a p-type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.

I_N = Current in N-type semiconductor
$=\left({\mathrm{\mu }}_{\mathrm{e}}{\mathrm{N}}_{\mathrm{e}}+{\mathrm{\mu }}_{\mathrm{h}}{\mathrm{n}}_{\mathrm{h}}\right)\mathrm{eAE}$
I_P = Current in P-type semiconductor
$=\left({\mathrm{\mu }}_{\mathrm{h}}{\mathrm{N}}_{\mathrm{h}}+{\mathrm{\mu }}_{\mathrm{e}}{\mathrm{n}}_{\mathrm{e}}\right)\mathrm{eAE}$
Now N_e = N_h and n_e  = n_h
Also ${\mathrm{\mu }}_{\mathrm{e}}>{\mathrm{\mu }}_{\mathrm{h}}\text{ and }{\mathrm{N}}_{\mathrm{e}}>>{\mathrm{n}}_{\mathrm{e}},{\mathrm{N}}_{\mathrm{h}}>>{\mathrm{n}}_{\mathrm{e}}$
Where N_e = electron concentration in N-type
N_h = Hole concentration in P-type
and N_e = N_h
n_h = hole concentration in N-type
n_e = Electron concentration in P-type
$\begin{array}{l}\therefore {\mathrm{l}}_{\mathrm{N}}-{\mathrm{l}}_{\mathrm{p}}=\left[\left({\mathrm{\mu }}_{\mathrm{e}}-{\mathrm{\mu }}_{\mathrm{h}}\right){\mathrm{N}}_{\mathrm{e}}+\left({\mathrm{\mu }}_{\mathrm{h}}-{\mathrm{\mu }}_{\mathrm{e}}\right){\mathrm{n}}_{\mathrm{e}}\right]\mathrm{eAE}\\ =\left({\mathrm{\mu }}_{\mathrm{e}}-{\mathrm{\mu }}_{\mathrm{h}}\right)\left({\mathrm{N}}_{\mathrm{e}}-{\mathrm{n}}_{\mathrm{e}}\right)\mathrm{eAE}\end{array}$
Since ${\text{μ}}_{\mathrm{e}}>{\mathrm{\mu }}_{\mathrm{h}} \mathrm{and} {\mathrm{N}}_{\mathrm{e}}>{\mathrm{n}}_{\mathrm{e}}$
We conclude I_N > I_P