A uniform beam HK of length \(10 \mathrm{~m}\) and weighing \(200 \mathrm{~N}\) is supported at both ends. A man weighing, \(100 \mathrm{~N}\) stands at a point \(P\) on the beam. if the reactions at \(\mathrm{H}\) and \(\mathrm{K}\) are respectively \(800 \mathrm{~N}\) and \(400 \mathrm{~N}\), then the distance HP is ____________