Answer
$96.7$ $K$
Work Step by Step
The formula for efficiency is $1-\frac{T_c}{T_h}$. Since efficiency is 0.4 and temperature of cold reservoir is 290 K, the temperature of the hot reservoir is $483.3 K$. To get an efficiency of 0.5, we need the temperature of the hot reservoir to be $580 K$, so an increase of $96.7 K$