A black body has maximum wavelength ${\lambda }_{\mathrm{m}}$ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be 

According to Wein's displacement law,

$\begin{array}{r}{\lambda }_{\mathrm{m}}\mathrm{T}=2.88\times {10}^{-3}\end{array}$

When $T=2000 K,$

${\lambda }_{\mathrm{m}}\left(2000\right)=2.88\times {10}^{-3}\dots \left(1\right)$

Where $T = 3000 K,$

${{\lambda }^{\text{'}}}_m\left(3000\right)=2.88\times {10}^{-3}\dots ..\left(2\right)$

Dividing (1) by (2), 

$\frac{2}{3}\frac{{\lambda }_m}{{\lambda }_m}=1\Rightarrow \frac{{\lambda }_m}{{\lambda }_m}=\frac{3}{2}={\lambda }_m^{\mathrm{\prime }}=\frac{2}{3}{\lambda }_m$