Answer
$1.07$ $hp$
Work Step by Step
All the symbols have the usual meaning.
$T_H=650K$
$T_C=290K$
Maximum efficiency: $\kappa=1-\dfrac{T_C}{T_H} \simeq 0.554$ (Carnot engine has maximum effeciency)
Heat taken in one cycle $=Q=1.5 \times 10^4$ $J$
Let $w$ be the work output per cycle.
$\kappa=\dfrac{w}{Q}=0.554 \Longrightarrow w \simeq 8310$ $J$
Number of cycles per second $=\dfrac{240}{60}=4$
Maximum power is work output per second.
Maximum power $=(8310 \times 4)$ $W=33240$ $W$
$746$ $W=1$ $hp$
$1$ $W=\dfrac{1}{746}$ $hp$
$33240$ $W \simeq 1.07$ $hp$
