If the temperature of  a black body increases by 50% then amount of  radiation emitted by it in a given time interval will                         

According to Stefan's law 

Energy emitted is proportional to ${\mathrm{T}}^4$.

Lets assume the initial temperature of black body be T, It is increased to 1.5T.

So, the percentage increase in radiation will be given by 

$\frac{{\mathrm{T}}_2^4-{\mathrm{T}}_1^4}{{ \mathrm{T}}_1^4}\times 100=\frac{{\left(1.5\mathrm{T}\right)}^4-{\mathrm{T}}^4}{{\mathrm{T}}^4}\times 100=406.25\%$