The power radiated by a black body is $P$ and it radiates maximum energy at wavelength, $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy $\frac{3}{4} \lambda_0$ , the power radiated by it becomes $nP$. The value of $n$ is

$\lambda_{\text{max}} T = \text{constant} \quad \text{(Wien's law)}$

$\textbf{So, } \lambda_{\text{max}_1} T_1 = \lambda_{\text{max}_2} T_2$

$\Rightarrow \lambda_0 T = \frac{3\lambda_0}{4} T'$

$\Rightarrow T' = \frac{4}{3}T$

$\textbf{So, } \frac{P_2}{P_1} = \left(\frac{T'}{T}\right)^4 = \left(\frac{4}{3}\right)^4 = \frac{256}{81}$